knowrohit07/gita_dataset · Datasets at Hugging Face

Chapter stringclasses 18 values	sentence_range stringlengths 3 9	Text stringlengths 7 7.34k
9	639-642	1 The microscope A simple magnifier or microscope is a converging lens of small focal length (Fig 9 23) In order to use such a lens as a microscope, the lens is held near the object, one focal length away or less, and the eye is positioned close to the lens on the other side
9	640-643	9 23) In order to use such a lens as a microscope, the lens is held near the object, one focal length away or less, and the eye is positioned close to the lens on the other side The idea is to get an erect, magnified and virtual image of the object at a distance so that it can be viewed comfortably, i
9	641-644	23) In order to use such a lens as a microscope, the lens is held near the object, one focal length away or less, and the eye is positioned close to the lens on the other side The idea is to get an erect, magnified and virtual image of the object at a distance so that it can be viewed comfortably, i e
9	642-645	In order to use such a lens as a microscope, the lens is held near the object, one focal length away or less, and the eye is positioned close to the lens on the other side The idea is to get an erect, magnified and virtual image of the object at a distance so that it can be viewed comfortably, i e , at 25 cm or more
9	643-646	The idea is to get an erect, magnified and virtual image of the object at a distance so that it can be viewed comfortably, i e , at 25 cm or more If the object is at a distance f, the image is at infinity
9	644-647	e , at 25 cm or more If the object is at a distance f, the image is at infinity However, if the object is at a distance slightly less FIGURE 9
9	645-648	, at 25 cm or more If the object is at a distance f, the image is at infinity However, if the object is at a distance slightly less FIGURE 9 22 Plot of angle of deviation (d) versus angle of incidence (i) for a triangular prism
9	646-649	If the object is at a distance f, the image is at infinity However, if the object is at a distance slightly less FIGURE 9 22 Plot of angle of deviation (d) versus angle of incidence (i) for a triangular prism Rationalised 2023-24 Ray Optics and Optical Instruments 241 than the focal length of the lens, the image is virtual and closer than infinity
9	647-650	However, if the object is at a distance slightly less FIGURE 9 22 Plot of angle of deviation (d) versus angle of incidence (i) for a triangular prism Rationalised 2023-24 Ray Optics and Optical Instruments 241 than the focal length of the lens, the image is virtual and closer than infinity Although the closest comfortable distance for viewing the image is when it is at the near point (distance D @ 25 cm), it causes some strain on the eye
9	648-651	22 Plot of angle of deviation (d) versus angle of incidence (i) for a triangular prism Rationalised 2023-24 Ray Optics and Optical Instruments 241 than the focal length of the lens, the image is virtual and closer than infinity Although the closest comfortable distance for viewing the image is when it is at the near point (distance D @ 25 cm), it causes some strain on the eye Therefore, the image formed at infinity is often considered most suitable for viewing by the relaxed eye
9	649-652	Rationalised 2023-24 Ray Optics and Optical Instruments 241 than the focal length of the lens, the image is virtual and closer than infinity Although the closest comfortable distance for viewing the image is when it is at the near point (distance D @ 25 cm), it causes some strain on the eye Therefore, the image formed at infinity is often considered most suitable for viewing by the relaxed eye We show both cases, the first in Fig
9	650-653	Although the closest comfortable distance for viewing the image is when it is at the near point (distance D @ 25 cm), it causes some strain on the eye Therefore, the image formed at infinity is often considered most suitable for viewing by the relaxed eye We show both cases, the first in Fig 9
9	651-654	Therefore, the image formed at infinity is often considered most suitable for viewing by the relaxed eye We show both cases, the first in Fig 9 23(a), and the second in Fig
9	652-655	We show both cases, the first in Fig 9 23(a), and the second in Fig 9
9	653-656	9 23(a), and the second in Fig 9 23(b) and (c)
9	654-657	23(a), and the second in Fig 9 23(b) and (c) The linear magnification m, for the image formed at the near point D, by a simple microscope can be obtained by using the relation FIGURE 9
9	655-658	9 23(b) and (c) The linear magnification m, for the image formed at the near point D, by a simple microscope can be obtained by using the relation FIGURE 9 23 A simple microscope; (a) the magnifying lens is located such that the image is at the near point, (b) the angle subtanded by the object, is the same as that at the near point, and (c) the object near the focal point of the lens; the image is far off but closer than infinity
9	656-659	23(b) and (c) The linear magnification m, for the image formed at the near point D, by a simple microscope can be obtained by using the relation FIGURE 9 23 A simple microscope; (a) the magnifying lens is located such that the image is at the near point, (b) the angle subtanded by the object, is the same as that at the near point, and (c) the object near the focal point of the lens; the image is far off but closer than infinity Rationalised 2023-24 Physics 242 m uv v v f fv = =     =     1 1 1 – – Now according to our sign convention, v is negative, and is equal in magnitude to D
9	657-660	The linear magnification m, for the image formed at the near point D, by a simple microscope can be obtained by using the relation FIGURE 9 23 A simple microscope; (a) the magnifying lens is located such that the image is at the near point, (b) the angle subtanded by the object, is the same as that at the near point, and (c) the object near the focal point of the lens; the image is far off but closer than infinity Rationalised 2023-24 Physics 242 m uv v v f fv = =     =     1 1 1 – – Now according to our sign convention, v is negative, and is equal in magnitude to D Thus, the magnification is m fD = +  1 (9
9	658-661	23 A simple microscope; (a) the magnifying lens is located such that the image is at the near point, (b) the angle subtanded by the object, is the same as that at the near point, and (c) the object near the focal point of the lens; the image is far off but closer than infinity Rationalised 2023-24 Physics 242 m uv v v f fv = =     =     1 1 1 – – Now according to our sign convention, v is negative, and is equal in magnitude to D Thus, the magnification is m fD = +  1 (9 39) Since D is about 25 cm, to have a magnification of six, one needs a convex lens of focal length, f = 5 cm
9	659-662	Rationalised 2023-24 Physics 242 m uv v v f fv = =     =     1 1 1 – – Now according to our sign convention, v is negative, and is equal in magnitude to D Thus, the magnification is m fD = +  1 (9 39) Since D is about 25 cm, to have a magnification of six, one needs a convex lens of focal length, f = 5 cm Note that m = h¢/h where h is the size of the object and h¢ the size of the image
9	660-663	Thus, the magnification is m fD = +  1 (9 39) Since D is about 25 cm, to have a magnification of six, one needs a convex lens of focal length, f = 5 cm Note that m = h¢/h where h is the size of the object and h¢ the size of the image This is also the ratio of the angle subtended by the image to that subtended by the object, if placed at D for comfortable viewing
9	661-664	39) Since D is about 25 cm, to have a magnification of six, one needs a convex lens of focal length, f = 5 cm Note that m = h¢/h where h is the size of the object and h¢ the size of the image This is also the ratio of the angle subtended by the image to that subtended by the object, if placed at D for comfortable viewing (Note that this is not the angle actually subtended by the object at the eye, which is h/u
9	662-665	Note that m = h¢/h where h is the size of the object and h¢ the size of the image This is also the ratio of the angle subtended by the image to that subtended by the object, if placed at D for comfortable viewing (Note that this is not the angle actually subtended by the object at the eye, which is h/u ) What a single-lens simple magnifier achieves is that it allows the object to be brought closer to the eye than D
9	663-666	This is also the ratio of the angle subtended by the image to that subtended by the object, if placed at D for comfortable viewing (Note that this is not the angle actually subtended by the object at the eye, which is h/u ) What a single-lens simple magnifier achieves is that it allows the object to be brought closer to the eye than D We will now find the magnification when the image is at infinity
9	664-667	(Note that this is not the angle actually subtended by the object at the eye, which is h/u ) What a single-lens simple magnifier achieves is that it allows the object to be brought closer to the eye than D We will now find the magnification when the image is at infinity In this case we will have to obtained the angular magnification
9	665-668	) What a single-lens simple magnifier achieves is that it allows the object to be brought closer to the eye than D We will now find the magnification when the image is at infinity In this case we will have to obtained the angular magnification Suppose the object has a height h
9	666-669	We will now find the magnification when the image is at infinity In this case we will have to obtained the angular magnification Suppose the object has a height h The maximum angle it can subtend, and be clearly visible (without a lens), is when it is at the near point, i
9	667-670	In this case we will have to obtained the angular magnification Suppose the object has a height h The maximum angle it can subtend, and be clearly visible (without a lens), is when it is at the near point, i e
9	668-671	Suppose the object has a height h The maximum angle it can subtend, and be clearly visible (without a lens), is when it is at the near point, i e , a distance D
9	669-672	The maximum angle it can subtend, and be clearly visible (without a lens), is when it is at the near point, i e , a distance D The angle subtended is then given by tan θo = Dh    » qo (9
9	670-673	e , a distance D The angle subtended is then given by tan θo = Dh    » qo (9 40) We now find the angle subtended at the eye by the image when the object is at u
9	671-674	, a distance D The angle subtended is then given by tan θo = Dh    » qo (9 40) We now find the angle subtended at the eye by the image when the object is at u From the relations h v m h u ′ = = we have the angle subtended by the image tan i h h v h v v u u θ ′ = = ⋅ = − − − »q
9	672-675	The angle subtended is then given by tan θo = Dh    » qo (9 40) We now find the angle subtended at the eye by the image when the object is at u From the relations h v m h u ′ = = we have the angle subtended by the image tan i h h v h v v u u θ ′ = = ⋅ = − − − »q The angle subtended by the object, when it is at u = –f
9	673-676	40) We now find the angle subtended at the eye by the image when the object is at u From the relations h v m h u ′ = = we have the angle subtended by the image tan i h h v h v v u u θ ′ = = ⋅ = − − − »q The angle subtended by the object, when it is at u = –f θi = fh   (9
9	674-677	From the relations h v m h u ′ = = we have the angle subtended by the image tan i h h v h v v u u θ ′ = = ⋅ = − − − »q The angle subtended by the object, when it is at u = –f θi = fh   (9 41) as is clear from Fig
9	675-678	The angle subtended by the object, when it is at u = –f θi = fh   (9 41) as is clear from Fig 9
9	676-679	θi = fh   (9 41) as is clear from Fig 9 23(c)
9	677-680	41) as is clear from Fig 9 23(c) The angular magnification is, therefore m D f i o =    θθ = (9
9	678-681	9 23(c) The angular magnification is, therefore m D f i o =    θθ = (9 42) This is one less than the magnification when the image is at the near point, Eq
9	679-682	23(c) The angular magnification is, therefore m D f i o =    θθ = (9 42) This is one less than the magnification when the image is at the near point, Eq (9
9	680-683	The angular magnification is, therefore m D f i o =    θθ = (9 42) This is one less than the magnification when the image is at the near point, Eq (9 39), but the viewing is more comfortable and the difference in magnification is usually small
9	681-684	42) This is one less than the magnification when the image is at the near point, Eq (9 39), but the viewing is more comfortable and the difference in magnification is usually small In subsequent discussions of optical instruments (microscope and telescope) we shall assume the image to be at infinity
9	682-685	(9 39), but the viewing is more comfortable and the difference in magnification is usually small In subsequent discussions of optical instruments (microscope and telescope) we shall assume the image to be at infinity Rationalised 2023-24 Ray Optics and Optical Instruments 243 A simple microscope has a limited maximum magnification (£ 9) for realistic focal lengths
9	683-686	39), but the viewing is more comfortable and the difference in magnification is usually small In subsequent discussions of optical instruments (microscope and telescope) we shall assume the image to be at infinity Rationalised 2023-24 Ray Optics and Optical Instruments 243 A simple microscope has a limited maximum magnification (£ 9) for realistic focal lengths For much larger magnifications, one uses two lenses, one compounding the effect of the other
9	684-687	In subsequent discussions of optical instruments (microscope and telescope) we shall assume the image to be at infinity Rationalised 2023-24 Ray Optics and Optical Instruments 243 A simple microscope has a limited maximum magnification (£ 9) for realistic focal lengths For much larger magnifications, one uses two lenses, one compounding the effect of the other This is known as a compound microscope
9	685-688	Rationalised 2023-24 Ray Optics and Optical Instruments 243 A simple microscope has a limited maximum magnification (£ 9) for realistic focal lengths For much larger magnifications, one uses two lenses, one compounding the effect of the other This is known as a compound microscope A schematic diagram of a compound microscope is shown in Fig
9	686-689	For much larger magnifications, one uses two lenses, one compounding the effect of the other This is known as a compound microscope A schematic diagram of a compound microscope is shown in Fig 9
9	687-690	This is known as a compound microscope A schematic diagram of a compound microscope is shown in Fig 9 24
9	688-691	A schematic diagram of a compound microscope is shown in Fig 9 24 The lens nearest the object, called the objective, forms a real, inverted, magnified image of the object
9	689-692	9 24 The lens nearest the object, called the objective, forms a real, inverted, magnified image of the object This serves as the object for the second lens, the eyepiece, which functions essentially like a simple microscope or magnifier, produces the final image, which is enlarged and virtual
9	690-693	24 The lens nearest the object, called the objective, forms a real, inverted, magnified image of the object This serves as the object for the second lens, the eyepiece, which functions essentially like a simple microscope or magnifier, produces the final image, which is enlarged and virtual The first inverted image is thus near (at or within) the focal plane of the eyepiece, at a distance appropriate for final image formation at infinity, or a little closer for image formation at the near point
9	691-694	The lens nearest the object, called the objective, forms a real, inverted, magnified image of the object This serves as the object for the second lens, the eyepiece, which functions essentially like a simple microscope or magnifier, produces the final image, which is enlarged and virtual The first inverted image is thus near (at or within) the focal plane of the eyepiece, at a distance appropriate for final image formation at infinity, or a little closer for image formation at the near point Clearly, the final image is inverted with respect to the original object
9	692-695	This serves as the object for the second lens, the eyepiece, which functions essentially like a simple microscope or magnifier, produces the final image, which is enlarged and virtual The first inverted image is thus near (at or within) the focal plane of the eyepiece, at a distance appropriate for final image formation at infinity, or a little closer for image formation at the near point Clearly, the final image is inverted with respect to the original object We now obtain the magnification due to a compound microscope
9	693-696	The first inverted image is thus near (at or within) the focal plane of the eyepiece, at a distance appropriate for final image formation at infinity, or a little closer for image formation at the near point Clearly, the final image is inverted with respect to the original object We now obtain the magnification due to a compound microscope The ray diagram of Fig
9	694-697	Clearly, the final image is inverted with respect to the original object We now obtain the magnification due to a compound microscope The ray diagram of Fig 9
9	695-698	We now obtain the magnification due to a compound microscope The ray diagram of Fig 9 24 shows that the (linear) magnification due to the objective, namely h¢/h, equals O o h L m h f ′ = = (9
9	696-699	The ray diagram of Fig 9 24 shows that the (linear) magnification due to the objective, namely h¢/h, equals O o h L m h f ′ = = (9 43) where we have used the result tanβ =     = ′   fh h L o Here h¢ is the size of the first image, the object size being h and fo being the focal length of the objective
9	697-700	9 24 shows that the (linear) magnification due to the objective, namely h¢/h, equals O o h L m h f ′ = = (9 43) where we have used the result tanβ =     = ′   fh h L o Here h¢ is the size of the first image, the object size being h and fo being the focal length of the objective The first image is formed near the focal point of the eyepiece
9	698-701	24 shows that the (linear) magnification due to the objective, namely h¢/h, equals O o h L m h f ′ = = (9 43) where we have used the result tanβ =     = ′   fh h L o Here h¢ is the size of the first image, the object size being h and fo being the focal length of the objective The first image is formed near the focal point of the eyepiece The distance L, i
9	699-702	43) where we have used the result tanβ =     = ′   fh h L o Here h¢ is the size of the first image, the object size being h and fo being the focal length of the objective The first image is formed near the focal point of the eyepiece The distance L, i e
9	700-703	The first image is formed near the focal point of the eyepiece The distance L, i e , the distance between the second focal point of the objective and the first focal point of the eyepiece (focal length fe) is called the tube length of the compound microscope
9	701-704	The distance L, i e , the distance between the second focal point of the objective and the first focal point of the eyepiece (focal length fe) is called the tube length of the compound microscope The world’s largest optical telescopes http://astro
9	702-705	e , the distance between the second focal point of the objective and the first focal point of the eyepiece (focal length fe) is called the tube length of the compound microscope The world’s largest optical telescopes http://astro nineplanets
9	703-706	, the distance between the second focal point of the objective and the first focal point of the eyepiece (focal length fe) is called the tube length of the compound microscope The world’s largest optical telescopes http://astro nineplanets org/bigeyes
9	704-707	The world’s largest optical telescopes http://astro nineplanets org/bigeyes html FIGURE 9
9	705-708	nineplanets org/bigeyes html FIGURE 9 24 Ray diagram for the formation of image by a compound microscope
9	706-709	org/bigeyes html FIGURE 9 24 Ray diagram for the formation of image by a compound microscope Rationalised 2023-24 Physics 244 As the first inverted image is near the focal point of the eyepiece, we use the result from the discussion above for the simple microscope to obtain the (angular) magnification me due to it [Eq
9	707-710	html FIGURE 9 24 Ray diagram for the formation of image by a compound microscope Rationalised 2023-24 Physics 244 As the first inverted image is near the focal point of the eyepiece, we use the result from the discussion above for the simple microscope to obtain the (angular) magnification me due to it [Eq (9
9	708-711	24 Ray diagram for the formation of image by a compound microscope Rationalised 2023-24 Physics 244 As the first inverted image is near the focal point of the eyepiece, we use the result from the discussion above for the simple microscope to obtain the (angular) magnification me due to it [Eq (9 39)], when the final image is formed at the near point, is m fD e e = 1+     [9
9	709-712	Rationalised 2023-24 Physics 244 As the first inverted image is near the focal point of the eyepiece, we use the result from the discussion above for the simple microscope to obtain the (angular) magnification me due to it [Eq (9 39)], when the final image is formed at the near point, is m fD e e = 1+     [9 44(a)] When the final image is formed at infinity, the angular magnification due to the eyepiece [Eq
9	710-713	(9 39)], when the final image is formed at the near point, is m fD e e = 1+     [9 44(a)] When the final image is formed at infinity, the angular magnification due to the eyepiece [Eq (9
9	711-714	39)], when the final image is formed at the near point, is m fD e e = 1+     [9 44(a)] When the final image is formed at infinity, the angular magnification due to the eyepiece [Eq (9 42)] is me = (D/fe ) [9
9	712-715	44(a)] When the final image is formed at infinity, the angular magnification due to the eyepiece [Eq (9 42)] is me = (D/fe ) [9 44(b)] Thus, the total magnification [(according to Eq
9	713-716	(9 42)] is me = (D/fe ) [9 44(b)] Thus, the total magnification [(according to Eq (9
9	714-717	42)] is me = (D/fe ) [9 44(b)] Thus, the total magnification [(according to Eq (9 33)], when the image is formed at infinity, is m m m fL fD o e o e = =         (9
9	715-718	44(b)] Thus, the total magnification [(according to Eq (9 33)], when the image is formed at infinity, is m m m fL fD o e o e = =         (9 45) Clearly, to achieve a large magnification of a small object (hence the name microscope), the objective and eyepiece should have small focal lengths
9	716-719	(9 33)], when the image is formed at infinity, is m m m fL fD o e o e = =         (9 45) Clearly, to achieve a large magnification of a small object (hence the name microscope), the objective and eyepiece should have small focal lengths In practice, it is difficult to make the focal length much smaller than 1 cm
9	717-720	33)], when the image is formed at infinity, is m m m fL fD o e o e = =         (9 45) Clearly, to achieve a large magnification of a small object (hence the name microscope), the objective and eyepiece should have small focal lengths In practice, it is difficult to make the focal length much smaller than 1 cm Also large lenses are required to make L large
9	718-721	45) Clearly, to achieve a large magnification of a small object (hence the name microscope), the objective and eyepiece should have small focal lengths In practice, it is difficult to make the focal length much smaller than 1 cm Also large lenses are required to make L large For example, with an objective with fo = 1
9	719-722	In practice, it is difficult to make the focal length much smaller than 1 cm Also large lenses are required to make L large For example, with an objective with fo = 1 0 cm, and an eyepiece with focal length fe = 2
9	720-723	Also large lenses are required to make L large For example, with an objective with fo = 1 0 cm, and an eyepiece with focal length fe = 2 0 cm, and a tube length of 20 cm, the magnification is m m m fL fD o e o e = =         20 25 250 1 2 � � � Various other factors such as illumination of the object, contribute to the quality and visibility of the image
9	721-724	For example, with an objective with fo = 1 0 cm, and an eyepiece with focal length fe = 2 0 cm, and a tube length of 20 cm, the magnification is m m m fL fD o e o e = =         20 25 250 1 2 � � � Various other factors such as illumination of the object, contribute to the quality and visibility of the image In modern microscopes, multi- component lenses are used for both the objective and the eyepiece to improve image quality by minimising various optical aberrations (defects) in lenses
9	722-725	0 cm, and an eyepiece with focal length fe = 2 0 cm, and a tube length of 20 cm, the magnification is m m m fL fD o e o e = =         20 25 250 1 2 � � � Various other factors such as illumination of the object, contribute to the quality and visibility of the image In modern microscopes, multi- component lenses are used for both the objective and the eyepiece to improve image quality by minimising various optical aberrations (defects) in lenses 9
9	723-726	0 cm, and a tube length of 20 cm, the magnification is m m m fL fD o e o e = =         20 25 250 1 2 � � � Various other factors such as illumination of the object, contribute to the quality and visibility of the image In modern microscopes, multi- component lenses are used for both the objective and the eyepiece to improve image quality by minimising various optical aberrations (defects) in lenses 9 7
9	724-727	In modern microscopes, multi- component lenses are used for both the objective and the eyepiece to improve image quality by minimising various optical aberrations (defects) in lenses 9 7 2 Telescope The telescope is used to provide angular magnification of distant objects (Fig
9	725-728	9 7 2 Telescope The telescope is used to provide angular magnification of distant objects (Fig 9
9	726-729	7 2 Telescope The telescope is used to provide angular magnification of distant objects (Fig 9 25)
9	727-730	2 Telescope The telescope is used to provide angular magnification of distant objects (Fig 9 25) It also has an objective and an eyepiece
9	728-731	9 25) It also has an objective and an eyepiece But here, the objective has a large focal length and a much larger aperture than the eyepiece
9	729-732	25) It also has an objective and an eyepiece But here, the objective has a large focal length and a much larger aperture than the eyepiece Light from a distant object enters the objective and a real image is formed in the tube at its second focal point
9	730-733	It also has an objective and an eyepiece But here, the objective has a large focal length and a much larger aperture than the eyepiece Light from a distant object enters the objective and a real image is formed in the tube at its second focal point The eyepiece magnifies this image producing a final inverted image
9	731-734	But here, the objective has a large focal length and a much larger aperture than the eyepiece Light from a distant object enters the objective and a real image is formed in the tube at its second focal point The eyepiece magnifies this image producing a final inverted image The magnifying power m is the ratio of the angle b subtended at the eye by the final image to the angle a which the object subtends at the lens or the eye
9	732-735	Light from a distant object enters the objective and a real image is formed in the tube at its second focal point The eyepiece magnifies this image producing a final inverted image The magnifying power m is the ratio of the angle b subtended at the eye by the final image to the angle a which the object subtends at the lens or the eye Hence
9	733-736	The eyepiece magnifies this image producing a final inverted image The magnifying power m is the ratio of the angle b subtended at the eye by the final image to the angle a which the object subtends at the lens or the eye Hence o o e e f f h m f h f � � � �� (9
9	734-737	The magnifying power m is the ratio of the angle b subtended at the eye by the final image to the angle a which the object subtends at the lens or the eye Hence o o e e f f h m f h f � � � �� (9 46) Rationalised 2023-24 Ray Optics and Optical Instruments 245 FIGURE 9
9	735-738	Hence o o e e f f h m f h f � � � �� (9 46) Rationalised 2023-24 Ray Optics and Optical Instruments 245 FIGURE 9 25 A refracting telescope
9	736-739	o o e e f f h m f h f � � � �� (9 46) Rationalised 2023-24 Ray Optics and Optical Instruments 245 FIGURE 9 25 A refracting telescope In this case, the length of the telescope tube is fo + fe
9	737-740	46) Rationalised 2023-24 Ray Optics and Optical Instruments 245 FIGURE 9 25 A refracting telescope In this case, the length of the telescope tube is fo + fe Terrestrial telescopes have, in addition, a pair of inverting lenses to make the final image erect
9	738-741	25 A refracting telescope In this case, the length of the telescope tube is fo + fe Terrestrial telescopes have, in addition, a pair of inverting lenses to make the final image erect Refracting telescopes can be used both for terrestrial and astronomical observations

9

639-642

1 The microscope A simple magnifier or microscope is a converging lens of small focal length (Fig 9 23) In order to use such a lens as a microscope, the lens is held near the object, one focal length away or less, and the eye is positioned close to the lens on the other side

9

640-643

9 23) In order to use such a lens as a microscope, the lens is held near the object, one focal length away or less, and the eye is positioned close to the lens on the other side The idea is to get an erect, magnified and virtual image of the object at a distance so that it can be viewed comfortably, i

9

641-644

23) In order to use such a lens as a microscope, the lens is held near the object, one focal length away or less, and the eye is positioned close to the lens on the other side The idea is to get an erect, magnified and virtual image of the object at a distance so that it can be viewed comfortably, i e

9

642-645

In order to use such a lens as a microscope, the lens is held near the object, one focal length away or less, and the eye is positioned close to the lens on the other side The idea is to get an erect, magnified and virtual image of the object at a distance so that it can be viewed comfortably, i e , at 25 cm or more

9

643-646

The idea is to get an erect, magnified and virtual image of the object at a distance so that it can be viewed comfortably, i e , at 25 cm or more If the object is at a distance f, the image is at infinity

9

644-647

e , at 25 cm or more If the object is at a distance f, the image is at infinity However, if the object is at a distance slightly less FIGURE 9

9

645-648

, at 25 cm or more If the object is at a distance f, the image is at infinity However, if the object is at a distance slightly less FIGURE 9 22 Plot of angle of deviation (d) versus angle of incidence (i) for a triangular prism

9

646-649

If the object is at a distance f, the image is at infinity However, if the object is at a distance slightly less FIGURE 9 22 Plot of angle of deviation (d) versus angle of incidence (i) for a triangular prism Rationalised 2023-24 Ray Optics and Optical Instruments 241 than the focal length of the lens, the image is virtual and closer than infinity

9

647-650

However, if the object is at a distance slightly less FIGURE 9 22 Plot of angle of deviation (d) versus angle of incidence (i) for a triangular prism Rationalised 2023-24 Ray Optics and Optical Instruments 241 than the focal length of the lens, the image is virtual and closer than infinity Although the closest comfortable distance for viewing the image is when it is at the near point (distance D @ 25 cm), it causes some strain on the eye

9

648-651

22 Plot of angle of deviation (d) versus angle of incidence (i) for a triangular prism Rationalised 2023-24 Ray Optics and Optical Instruments 241 than the focal length of the lens, the image is virtual and closer than infinity Although the closest comfortable distance for viewing the image is when it is at the near point (distance D @ 25 cm), it causes some strain on the eye Therefore, the image formed at infinity is often considered most suitable for viewing by the relaxed eye

9

649-652

Rationalised 2023-24 Ray Optics and Optical Instruments 241 than the focal length of the lens, the image is virtual and closer than infinity Although the closest comfortable distance for viewing the image is when it is at the near point (distance D @ 25 cm), it causes some strain on the eye Therefore, the image formed at infinity is often considered most suitable for viewing by the relaxed eye We show both cases, the first in Fig

9

650-653

Although the closest comfortable distance for viewing the image is when it is at the near point (distance D @ 25 cm), it causes some strain on the eye Therefore, the image formed at infinity is often considered most suitable for viewing by the relaxed eye We show both cases, the first in Fig 9

9

651-654

Therefore, the image formed at infinity is often considered most suitable for viewing by the relaxed eye We show both cases, the first in Fig 9 23(a), and the second in Fig

9

652-655

We show both cases, the first in Fig 9 23(a), and the second in Fig 9

9

653-656

9 23(a), and the second in Fig 9 23(b) and (c)

9

654-657

23(a), and the second in Fig 9 23(b) and (c) The linear magnification m, for the image formed at the near point D, by a simple microscope can be obtained by using the relation FIGURE 9

9

655-658

9 23(b) and (c) The linear magnification m, for the image formed at the near point D, by a simple microscope can be obtained by using the relation FIGURE 9 23 A simple microscope; (a) the magnifying lens is located such that the image is at the near point, (b) the angle subtanded by the object, is the same as that at the near point, and (c) the object near the focal point of the lens; the image is far off but closer than infinity

9

656-659

23(b) and (c) The linear magnification m, for the image formed at the near point D, by a simple microscope can be obtained by using the relation FIGURE 9 23 A simple microscope; (a) the magnifying lens is located such that the image is at the near point, (b) the angle subtanded by the object, is the same as that at the near point, and (c) the object near the focal point of the lens; the image is far off but closer than infinity Rationalised 2023-24 Physics 242 m uv v v f fv = =     =     1 1 1 – – Now according to our sign convention, v is negative, and is equal in magnitude to D

9

657-660

The linear magnification m, for the image formed at the near point D, by a simple microscope can be obtained by using the relation FIGURE 9 23 A simple microscope; (a) the magnifying lens is located such that the image is at the near point, (b) the angle subtanded by the object, is the same as that at the near point, and (c) the object near the focal point of the lens; the image is far off but closer than infinity Rationalised 2023-24 Physics 242 m uv v v f fv = =     =     1 1 1 – – Now according to our sign convention, v is negative, and is equal in magnitude to D Thus, the magnification is m fD = +  1 (9

9

658-661

23 A simple microscope; (a) the magnifying lens is located such that the image is at the near point, (b) the angle subtanded by the object, is the same as that at the near point, and (c) the object near the focal point of the lens; the image is far off but closer than infinity Rationalised 2023-24 Physics 242 m uv v v f fv = =     =     1 1 1 – – Now according to our sign convention, v is negative, and is equal in magnitude to D Thus, the magnification is m fD = +  1 (9 39) Since D is about 25 cm, to have a magnification of six, one needs a convex lens of focal length, f = 5 cm

9

659-662

Rationalised 2023-24 Physics 242 m uv v v f fv = =     =     1 1 1 – – Now according to our sign convention, v is negative, and is equal in magnitude to D Thus, the magnification is m fD = +  1 (9 39) Since D is about 25 cm, to have a magnification of six, one needs a convex lens of focal length, f = 5 cm Note that m = h¢/h where h is the size of the object and h¢ the size of the image

9

660-663

Thus, the magnification is m fD = +  1 (9 39) Since D is about 25 cm, to have a magnification of six, one needs a convex lens of focal length, f = 5 cm Note that m = h¢/h where h is the size of the object and h¢ the size of the image This is also the ratio of the angle subtended by the image to that subtended by the object, if placed at D for comfortable viewing

9

661-664

39) Since D is about 25 cm, to have a magnification of six, one needs a convex lens of focal length, f = 5 cm Note that m = h¢/h where h is the size of the object and h¢ the size of the image This is also the ratio of the angle subtended by the image to that subtended by the object, if placed at D for comfortable viewing (Note that this is not the angle actually subtended by the object at the eye, which is h/u

9

662-665

Note that m = h¢/h where h is the size of the object and h¢ the size of the image This is also the ratio of the angle subtended by the image to that subtended by the object, if placed at D for comfortable viewing (Note that this is not the angle actually subtended by the object at the eye, which is h/u ) What a single-lens simple magnifier achieves is that it allows the object to be brought closer to the eye than D

9

663-666

This is also the ratio of the angle subtended by the image to that subtended by the object, if placed at D for comfortable viewing (Note that this is not the angle actually subtended by the object at the eye, which is h/u ) What a single-lens simple magnifier achieves is that it allows the object to be brought closer to the eye than D We will now find the magnification when the image is at infinity

9

664-667

(Note that this is not the angle actually subtended by the object at the eye, which is h/u ) What a single-lens simple magnifier achieves is that it allows the object to be brought closer to the eye than D We will now find the magnification when the image is at infinity In this case we will have to obtained the angular magnification

9

665-668

) What a single-lens simple magnifier achieves is that it allows the object to be brought closer to the eye than D We will now find the magnification when the image is at infinity In this case we will have to obtained the angular magnification Suppose the object has a height h

9

666-669

We will now find the magnification when the image is at infinity In this case we will have to obtained the angular magnification Suppose the object has a height h The maximum angle it can subtend, and be clearly visible (without a lens), is when it is at the near point, i

9

667-670

In this case we will have to obtained the angular magnification Suppose the object has a height h The maximum angle it can subtend, and be clearly visible (without a lens), is when it is at the near point, i e

9

668-671

Suppose the object has a height h The maximum angle it can subtend, and be clearly visible (without a lens), is when it is at the near point, i e , a distance D

9

669-672

The maximum angle it can subtend, and be clearly visible (without a lens), is when it is at the near point, i e , a distance D The angle subtended is then given by tan θo = Dh    » qo (9

9

670-673

e , a distance D The angle subtended is then given by tan θo = Dh    » qo (9 40) We now find the angle subtended at the eye by the image when the object is at u

9

671-674

, a distance D The angle subtended is then given by tan θo = Dh    » qo (9 40) We now find the angle subtended at the eye by the image when the object is at u From the relations h v m h u ′ = = we have the angle subtended by the image tan i h h v h v v u u θ ′ = = ⋅ = − − − »q

9

672-675

The angle subtended is then given by tan θo = Dh    » qo (9 40) We now find the angle subtended at the eye by the image when the object is at u From the relations h v m h u ′ = = we have the angle subtended by the image tan i h h v h v v u u θ ′ = = ⋅ = − − − »q The angle subtended by the object, when it is at u = –f

9

673-676

40) We now find the angle subtended at the eye by the image when the object is at u From the relations h v m h u ′ = = we have the angle subtended by the image tan i h h v h v v u u θ ′ = = ⋅ = − − − »q The angle subtended by the object, when it is at u = –f θi = fh   (9

9

674-677

From the relations h v m h u ′ = = we have the angle subtended by the image tan i h h v h v v u u θ ′ = = ⋅ = − − − »q The angle subtended by the object, when it is at u = –f θi = fh   (9 41) as is clear from Fig

9

675-678

The angle subtended by the object, when it is at u = –f θi = fh   (9 41) as is clear from Fig 9

9

676-679

θi = fh   (9 41) as is clear from Fig 9 23(c)

9

677-680

41) as is clear from Fig 9 23(c) The angular magnification is, therefore m D f i o =    θθ = (9

9

678-681

9 23(c) The angular magnification is, therefore m D f i o =    θθ = (9 42) This is one less than the magnification when the image is at the near point, Eq

9

679-682

23(c) The angular magnification is, therefore m D f i o =    θθ = (9 42) This is one less than the magnification when the image is at the near point, Eq (9

9

680-683

The angular magnification is, therefore m D f i o =    θθ = (9 42) This is one less than the magnification when the image is at the near point, Eq (9 39), but the viewing is more comfortable and the difference in magnification is usually small

9

681-684

42) This is one less than the magnification when the image is at the near point, Eq (9 39), but the viewing is more comfortable and the difference in magnification is usually small In subsequent discussions of optical instruments (microscope and telescope) we shall assume the image to be at infinity

9

682-685

(9 39), but the viewing is more comfortable and the difference in magnification is usually small In subsequent discussions of optical instruments (microscope and telescope) we shall assume the image to be at infinity Rationalised 2023-24 Ray Optics and Optical Instruments 243 A simple microscope has a limited maximum magnification (£ 9) for realistic focal lengths

9

683-686

39), but the viewing is more comfortable and the difference in magnification is usually small In subsequent discussions of optical instruments (microscope and telescope) we shall assume the image to be at infinity Rationalised 2023-24 Ray Optics and Optical Instruments 243 A simple microscope has a limited maximum magnification (£ 9) for realistic focal lengths For much larger magnifications, one uses two lenses, one compounding the effect of the other

9

684-687

In subsequent discussions of optical instruments (microscope and telescope) we shall assume the image to be at infinity Rationalised 2023-24 Ray Optics and Optical Instruments 243 A simple microscope has a limited maximum magnification (£ 9) for realistic focal lengths For much larger magnifications, one uses two lenses, one compounding the effect of the other This is known as a compound microscope

9

685-688

Rationalised 2023-24 Ray Optics and Optical Instruments 243 A simple microscope has a limited maximum magnification (£ 9) for realistic focal lengths For much larger magnifications, one uses two lenses, one compounding the effect of the other This is known as a compound microscope A schematic diagram of a compound microscope is shown in Fig

9

686-689

For much larger magnifications, one uses two lenses, one compounding the effect of the other This is known as a compound microscope A schematic diagram of a compound microscope is shown in Fig 9

9

687-690

This is known as a compound microscope A schematic diagram of a compound microscope is shown in Fig 9 24

9

688-691

A schematic diagram of a compound microscope is shown in Fig 9 24 The lens nearest the object, called the objective, forms a real, inverted, magnified image of the object

9

689-692

9 24 The lens nearest the object, called the objective, forms a real, inverted, magnified image of the object This serves as the object for the second lens, the eyepiece, which functions essentially like a simple microscope or magnifier, produces the final image, which is enlarged and virtual

9

690-693

24 The lens nearest the object, called the objective, forms a real, inverted, magnified image of the object This serves as the object for the second lens, the eyepiece, which functions essentially like a simple microscope or magnifier, produces the final image, which is enlarged and virtual The first inverted image is thus near (at or within) the focal plane of the eyepiece, at a distance appropriate for final image formation at infinity, or a little closer for image formation at the near point

9

691-694

The lens nearest the object, called the objective, forms a real, inverted, magnified image of the object This serves as the object for the second lens, the eyepiece, which functions essentially like a simple microscope or magnifier, produces the final image, which is enlarged and virtual The first inverted image is thus near (at or within) the focal plane of the eyepiece, at a distance appropriate for final image formation at infinity, or a little closer for image formation at the near point Clearly, the final image is inverted with respect to the original object

9

692-695

This serves as the object for the second lens, the eyepiece, which functions essentially like a simple microscope or magnifier, produces the final image, which is enlarged and virtual The first inverted image is thus near (at or within) the focal plane of the eyepiece, at a distance appropriate for final image formation at infinity, or a little closer for image formation at the near point Clearly, the final image is inverted with respect to the original object We now obtain the magnification due to a compound microscope

9

693-696

The first inverted image is thus near (at or within) the focal plane of the eyepiece, at a distance appropriate for final image formation at infinity, or a little closer for image formation at the near point Clearly, the final image is inverted with respect to the original object We now obtain the magnification due to a compound microscope The ray diagram of Fig

9

694-697

Clearly, the final image is inverted with respect to the original object We now obtain the magnification due to a compound microscope The ray diagram of Fig 9

9

695-698

We now obtain the magnification due to a compound microscope The ray diagram of Fig 9 24 shows that the (linear) magnification due to the objective, namely h¢/h, equals O o h L m h f ′ = = (9

9

696-699

The ray diagram of Fig 9 24 shows that the (linear) magnification due to the objective, namely h¢/h, equals O o h L m h f ′ = = (9 43) where we have used the result tanβ =     = ′   fh h L o Here h¢ is the size of the first image, the object size being h and fo being the focal length of the objective

9

697-700

9 24 shows that the (linear) magnification due to the objective, namely h¢/h, equals O o h L m h f ′ = = (9 43) where we have used the result tanβ =     = ′   fh h L o Here h¢ is the size of the first image, the object size being h and fo being the focal length of the objective The first image is formed near the focal point of the eyepiece

9

698-701

24 shows that the (linear) magnification due to the objective, namely h¢/h, equals O o h L m h f ′ = = (9 43) where we have used the result tanβ =     = ′   fh h L o Here h¢ is the size of the first image, the object size being h and fo being the focal length of the objective The first image is formed near the focal point of the eyepiece The distance L, i

9

699-702

43) where we have used the result tanβ =     = ′   fh h L o Here h¢ is the size of the first image, the object size being h and fo being the focal length of the objective The first image is formed near the focal point of the eyepiece The distance L, i e

9

700-703

The first image is formed near the focal point of the eyepiece The distance L, i e , the distance between the second focal point of the objective and the first focal point of the eyepiece (focal length fe) is called the tube length of the compound microscope

9

701-704

The distance L, i e , the distance between the second focal point of the objective and the first focal point of the eyepiece (focal length fe) is called the tube length of the compound microscope The world’s largest optical telescopes http://astro

9

702-705

e , the distance between the second focal point of the objective and the first focal point of the eyepiece (focal length fe) is called the tube length of the compound microscope The world’s largest optical telescopes http://astro nineplanets

9

703-706

, the distance between the second focal point of the objective and the first focal point of the eyepiece (focal length fe) is called the tube length of the compound microscope The world’s largest optical telescopes http://astro nineplanets org/bigeyes

9

704-707

The world’s largest optical telescopes http://astro nineplanets org/bigeyes html FIGURE 9

9

705-708

nineplanets org/bigeyes html FIGURE 9 24 Ray diagram for the formation of image by a compound microscope

9

706-709

org/bigeyes html FIGURE 9 24 Ray diagram for the formation of image by a compound microscope Rationalised 2023-24 Physics 244 As the first inverted image is near the focal point of the eyepiece, we use the result from the discussion above for the simple microscope to obtain the (angular) magnification me due to it [Eq

9

707-710

html FIGURE 9 24 Ray diagram for the formation of image by a compound microscope Rationalised 2023-24 Physics 244 As the first inverted image is near the focal point of the eyepiece, we use the result from the discussion above for the simple microscope to obtain the (angular) magnification me due to it [Eq (9

9

708-711

24 Ray diagram for the formation of image by a compound microscope Rationalised 2023-24 Physics 244 As the first inverted image is near the focal point of the eyepiece, we use the result from the discussion above for the simple microscope to obtain the (angular) magnification me due to it [Eq (9 39)], when the final image is formed at the near point, is m fD e e = 1+     [9

9

709-712

Rationalised 2023-24 Physics 244 As the first inverted image is near the focal point of the eyepiece, we use the result from the discussion above for the simple microscope to obtain the (angular) magnification me due to it [Eq (9 39)], when the final image is formed at the near point, is m fD e e = 1+     [9 44(a)] When the final image is formed at infinity, the angular magnification due to the eyepiece [Eq

9

710-713

(9 39)], when the final image is formed at the near point, is m fD e e = 1+     [9 44(a)] When the final image is formed at infinity, the angular magnification due to the eyepiece [Eq (9

9

711-714

39)], when the final image is formed at the near point, is m fD e e = 1+     [9 44(a)] When the final image is formed at infinity, the angular magnification due to the eyepiece [Eq (9 42)] is me = (D/fe ) [9

9

712-715

44(a)] When the final image is formed at infinity, the angular magnification due to the eyepiece [Eq (9 42)] is me = (D/fe ) [9 44(b)] Thus, the total magnification [(according to Eq

9

713-716

(9 42)] is me = (D/fe ) [9 44(b)] Thus, the total magnification [(according to Eq (9

9

714-717

42)] is me = (D/fe ) [9 44(b)] Thus, the total magnification [(according to Eq (9 33)], when the image is formed at infinity, is m m m fL fD o e o e = =         (9

9

715-718

44(b)] Thus, the total magnification [(according to Eq (9 33)], when the image is formed at infinity, is m m m fL fD o e o e = =         (9 45) Clearly, to achieve a large magnification of a small object (hence the name microscope), the objective and eyepiece should have small focal lengths

9

716-719

(9 33)], when the image is formed at infinity, is m m m fL fD o e o e = =         (9 45) Clearly, to achieve a large magnification of a small object (hence the name microscope), the objective and eyepiece should have small focal lengths In practice, it is difficult to make the focal length much smaller than 1 cm

9

717-720

33)], when the image is formed at infinity, is m m m fL fD o e o e = =         (9 45) Clearly, to achieve a large magnification of a small object (hence the name microscope), the objective and eyepiece should have small focal lengths In practice, it is difficult to make the focal length much smaller than 1 cm Also large lenses are required to make L large

9

718-721

45) Clearly, to achieve a large magnification of a small object (hence the name microscope), the objective and eyepiece should have small focal lengths In practice, it is difficult to make the focal length much smaller than 1 cm Also large lenses are required to make L large For example, with an objective with fo = 1

9

719-722

In practice, it is difficult to make the focal length much smaller than 1 cm Also large lenses are required to make L large For example, with an objective with fo = 1 0 cm, and an eyepiece with focal length fe = 2

9

720-723

Also large lenses are required to make L large For example, with an objective with fo = 1 0 cm, and an eyepiece with focal length fe = 2 0 cm, and a tube length of 20 cm, the magnification is m m m fL fD o e o e = =         20 25 250 1 2 � � � Various other factors such as illumination of the object, contribute to the quality and visibility of the image

9

721-724

For example, with an objective with fo = 1 0 cm, and an eyepiece with focal length fe = 2 0 cm, and a tube length of 20 cm, the magnification is m m m fL fD o e o e = =         20 25 250 1 2 � � � Various other factors such as illumination of the object, contribute to the quality and visibility of the image In modern microscopes, multi- component lenses are used for both the objective and the eyepiece to improve image quality by minimising various optical aberrations (defects) in lenses

9

722-725

0 cm, and an eyepiece with focal length fe = 2 0 cm, and a tube length of 20 cm, the magnification is m m m fL fD o e o e = =         20 25 250 1 2 � � � Various other factors such as illumination of the object, contribute to the quality and visibility of the image In modern microscopes, multi- component lenses are used for both the objective and the eyepiece to improve image quality by minimising various optical aberrations (defects) in lenses 9

9

723-726

0 cm, and a tube length of 20 cm, the magnification is m m m fL fD o e o e = =         20 25 250 1 2 � � � Various other factors such as illumination of the object, contribute to the quality and visibility of the image In modern microscopes, multi- component lenses are used for both the objective and the eyepiece to improve image quality by minimising various optical aberrations (defects) in lenses 9 7

9

724-727

In modern microscopes, multi- component lenses are used for both the objective and the eyepiece to improve image quality by minimising various optical aberrations (defects) in lenses 9 7 2 Telescope The telescope is used to provide angular magnification of distant objects (Fig

9

725-728

9 7 2 Telescope The telescope is used to provide angular magnification of distant objects (Fig 9

9

726-729

7 2 Telescope The telescope is used to provide angular magnification of distant objects (Fig 9 25)

9

727-730

2 Telescope The telescope is used to provide angular magnification of distant objects (Fig 9 25) It also has an objective and an eyepiece

9

728-731

9 25) It also has an objective and an eyepiece But here, the objective has a large focal length and a much larger aperture than the eyepiece

9

729-732

25) It also has an objective and an eyepiece But here, the objective has a large focal length and a much larger aperture than the eyepiece Light from a distant object enters the objective and a real image is formed in the tube at its second focal point

9

730-733

It also has an objective and an eyepiece But here, the objective has a large focal length and a much larger aperture than the eyepiece Light from a distant object enters the objective and a real image is formed in the tube at its second focal point The eyepiece magnifies this image producing a final inverted image

9

731-734

But here, the objective has a large focal length and a much larger aperture than the eyepiece Light from a distant object enters the objective and a real image is formed in the tube at its second focal point The eyepiece magnifies this image producing a final inverted image The magnifying power m is the ratio of the angle b subtended at the eye by the final image to the angle a which the object subtends at the lens or the eye

9

732-735

Light from a distant object enters the objective and a real image is formed in the tube at its second focal point The eyepiece magnifies this image producing a final inverted image The magnifying power m is the ratio of the angle b subtended at the eye by the final image to the angle a which the object subtends at the lens or the eye Hence

9

733-736

The eyepiece magnifies this image producing a final inverted image The magnifying power m is the ratio of the angle b subtended at the eye by the final image to the angle a which the object subtends at the lens or the eye Hence o o e e f f h m f h f � � � �� (9

9

734-737

The magnifying power m is the ratio of the angle b subtended at the eye by the final image to the angle a which the object subtends at the lens or the eye Hence o o e e f f h m f h f � � � �� (9 46) Rationalised 2023-24 Ray Optics and Optical Instruments 245 FIGURE 9

9

735-738

Hence o o e e f f h m f h f � � � �� (9 46) Rationalised 2023-24 Ray Optics and Optical Instruments 245 FIGURE 9 25 A refracting telescope

9

736-739

o o e e f f h m f h f � � � �� (9 46) Rationalised 2023-24 Ray Optics and Optical Instruments 245 FIGURE 9 25 A refracting telescope In this case, the length of the telescope tube is fo + fe

9

737-740

46) Rationalised 2023-24 Ray Optics and Optical Instruments 245 FIGURE 9 25 A refracting telescope In this case, the length of the telescope tube is fo + fe Terrestrial telescopes have, in addition, a pair of inverting lenses to make the final image erect

9

738-741

25 A refracting telescope In this case, the length of the telescope tube is fo + fe Terrestrial telescopes have, in addition, a pair of inverting lenses to make the final image erect Refracting telescopes can be used both for terrestrial and astronomical observations