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9
539-542
2 cm 9 5 4 Combination of thin lenses in contact Consider two lenses A and B of focal length f1 and f2 placed in contact with each other
9
540-543
9 5 4 Combination of thin lenses in contact Consider two lenses A and B of focal length f1 and f2 placed in contact with each other Let the object be placed at a point O beyond the focus of the first lens A (Fig
9
541-544
5 4 Combination of thin lenses in contact Consider two lenses A and B of focal length f1 and f2 placed in contact with each other Let the object be placed at a point O beyond the focus of the first lens A (Fig 9
9
542-545
4 Combination of thin lenses in contact Consider two lenses A and B of focal length f1 and f2 placed in contact with each other Let the object be placed at a point O beyond the focus of the first lens A (Fig 9 19)
9
543-546
Let the object be placed at a point O beyond the focus of the first lens A (Fig 9 19) The first lens produces an image at I1
9
544-547
9 19) The first lens produces an image at I1 Since image I1 is real, it serves as a virtual object for the second lens B, producing the final image at I
9
545-548
19) The first lens produces an image at I1 Since image I1 is real, it serves as a virtual object for the second lens B, producing the final image at I It must, however, be borne in mind that formation of image by the first lens is presumed only to facilitate determination of the position of the final image
9
546-549
The first lens produces an image at I1 Since image I1 is real, it serves as a virtual object for the second lens B, producing the final image at I It must, however, be borne in mind that formation of image by the first lens is presumed only to facilitate determination of the position of the final image In fact, the direction of rays emerging from the first lens gets modified in accordance with the angle at which they strike the second lens
9
547-550
Since image I1 is real, it serves as a virtual object for the second lens B, producing the final image at I It must, however, be borne in mind that formation of image by the first lens is presumed only to facilitate determination of the position of the final image In fact, the direction of rays emerging from the first lens gets modified in accordance with the angle at which they strike the second lens Since the lenses are thin, we assume the optical centres of the lenses to be coincident
9
548-551
It must, however, be borne in mind that formation of image by the first lens is presumed only to facilitate determination of the position of the final image In fact, the direction of rays emerging from the first lens gets modified in accordance with the angle at which they strike the second lens Since the lenses are thin, we assume the optical centres of the lenses to be coincident Let this central point be denoted by P
9
549-552
In fact, the direction of rays emerging from the first lens gets modified in accordance with the angle at which they strike the second lens Since the lenses are thin, we assume the optical centres of the lenses to be coincident Let this central point be denoted by P For the image formed by the first lens A, we get 1 1 1 1 1 v u f − = (9
9
550-553
Since the lenses are thin, we assume the optical centres of the lenses to be coincident Let this central point be denoted by P For the image formed by the first lens A, we get 1 1 1 1 1 v u f − = (9 27) For the image formed by the second lens B, we get 1 2 1 1 1 v v f − = (9
9
551-554
Let this central point be denoted by P For the image formed by the first lens A, we get 1 1 1 1 1 v u f − = (9 27) For the image formed by the second lens B, we get 1 2 1 1 1 v v f − = (9 28) Adding Eqs
9
552-555
For the image formed by the first lens A, we get 1 1 1 1 1 v u f − = (9 27) For the image formed by the second lens B, we get 1 2 1 1 1 v v f − = (9 28) Adding Eqs (9
9
553-556
27) For the image formed by the second lens B, we get 1 2 1 1 1 v v f − = (9 28) Adding Eqs (9 27) and (9
9
554-557
28) Adding Eqs (9 27) and (9 28), we get 1 2 1 1 1 1 v u f f − = + (9
9
555-558
(9 27) and (9 28), we get 1 2 1 1 1 1 v u f f − = + (9 29) If the two lens-system is regarded as equivalent to a single lens of focal length f, we have FIGURE 9
9
556-559
27) and (9 28), we get 1 2 1 1 1 1 v u f f − = + (9 29) If the two lens-system is regarded as equivalent to a single lens of focal length f, we have FIGURE 9 19 Image formation by a combination of two thin lenses in contact
9
557-560
28), we get 1 2 1 1 1 1 v u f f − = + (9 29) If the two lens-system is regarded as equivalent to a single lens of focal length f, we have FIGURE 9 19 Image formation by a combination of two thin lenses in contact EXAMPLE 9
9
558-561
29) If the two lens-system is regarded as equivalent to a single lens of focal length f, we have FIGURE 9 19 Image formation by a combination of two thin lenses in contact EXAMPLE 9 7 Rationalised 2023-24 Physics 238 EXAMPLE 9
9
559-562
19 Image formation by a combination of two thin lenses in contact EXAMPLE 9 7 Rationalised 2023-24 Physics 238 EXAMPLE 9 8 1 1 1 v u f − = so that we get 1 2 1 1 1 f f f = + (9
9
560-563
EXAMPLE 9 7 Rationalised 2023-24 Physics 238 EXAMPLE 9 8 1 1 1 v u f − = so that we get 1 2 1 1 1 f f f = + (9 30) The derivation is valid for any number of thin lenses in contact
9
561-564
7 Rationalised 2023-24 Physics 238 EXAMPLE 9 8 1 1 1 v u f − = so that we get 1 2 1 1 1 f f f = + (9 30) The derivation is valid for any number of thin lenses in contact If several thin lenses of focal length f1, f2, f3,
9
562-565
8 1 1 1 v u f − = so that we get 1 2 1 1 1 f f f = + (9 30) The derivation is valid for any number of thin lenses in contact If several thin lenses of focal length f1, f2, f3, are in contact, the effective focal length of their combination is given by 1 2 3 1 1 1 1 f f f f = + + + … (9
9
563-566
30) The derivation is valid for any number of thin lenses in contact If several thin lenses of focal length f1, f2, f3, are in contact, the effective focal length of their combination is given by 1 2 3 1 1 1 1 f f f f = + + + … (9 31) In terms of power, Eq
9
564-567
If several thin lenses of focal length f1, f2, f3, are in contact, the effective focal length of their combination is given by 1 2 3 1 1 1 1 f f f f = + + + … (9 31) In terms of power, Eq (9
9
565-568
are in contact, the effective focal length of their combination is given by 1 2 3 1 1 1 1 f f f f = + + + … (9 31) In terms of power, Eq (9 31) can be written as P = P1 + P2 + P3 + … (9
9
566-569
31) In terms of power, Eq (9 31) can be written as P = P1 + P2 + P3 + … (9 32) where P is the net power of the lens combination
9
567-570
(9 31) can be written as P = P1 + P2 + P3 + … (9 32) where P is the net power of the lens combination Note that the sum in Eq
9
568-571
31) can be written as P = P1 + P2 + P3 + … (9 32) where P is the net power of the lens combination Note that the sum in Eq (9
9
569-572
32) where P is the net power of the lens combination Note that the sum in Eq (9 32) is an algebraic sum of individual powers, so some of the terms on the right side may be positive (for convex lenses) and some negative (for concave lenses)
9
570-573
Note that the sum in Eq (9 32) is an algebraic sum of individual powers, so some of the terms on the right side may be positive (for convex lenses) and some negative (for concave lenses) Combination of lenses helps to obtain diverging or converging lenses of desired magnification
9
571-574
(9 32) is an algebraic sum of individual powers, so some of the terms on the right side may be positive (for convex lenses) and some negative (for concave lenses) Combination of lenses helps to obtain diverging or converging lenses of desired magnification It also enhances sharpness of the image
9
572-575
32) is an algebraic sum of individual powers, so some of the terms on the right side may be positive (for convex lenses) and some negative (for concave lenses) Combination of lenses helps to obtain diverging or converging lenses of desired magnification It also enhances sharpness of the image Since the image formed by the first lens becomes the object for the second, Eq
9
573-576
Combination of lenses helps to obtain diverging or converging lenses of desired magnification It also enhances sharpness of the image Since the image formed by the first lens becomes the object for the second, Eq (9
9
574-577
It also enhances sharpness of the image Since the image formed by the first lens becomes the object for the second, Eq (9 25) implies that the total magnification m of the combination is a product of magnification (m1, m 2, m 3,
9
575-578
Since the image formed by the first lens becomes the object for the second, Eq (9 25) implies that the total magnification m of the combination is a product of magnification (m1, m 2, m 3, ) of individual lenses m = m1 m2 m3
9
576-579
(9 25) implies that the total magnification m of the combination is a product of magnification (m1, m 2, m 3, ) of individual lenses m = m1 m2 m3 (9
9
577-580
25) implies that the total magnification m of the combination is a product of magnification (m1, m 2, m 3, ) of individual lenses m = m1 m2 m3 (9 33) Such a system of combination of lenses is commonly used in designing lenses for cameras, microscopes, telescopes and other optical instruments
9
578-581
) of individual lenses m = m1 m2 m3 (9 33) Such a system of combination of lenses is commonly used in designing lenses for cameras, microscopes, telescopes and other optical instruments Example 9
9
579-582
(9 33) Such a system of combination of lenses is commonly used in designing lenses for cameras, microscopes, telescopes and other optical instruments Example 9 8 Find the position of the image formed by the lens combination given in the Fig
9
580-583
33) Such a system of combination of lenses is commonly used in designing lenses for cameras, microscopes, telescopes and other optical instruments Example 9 8 Find the position of the image formed by the lens combination given in the Fig 9
9
581-584
Example 9 8 Find the position of the image formed by the lens combination given in the Fig 9 20
9
582-585
8 Find the position of the image formed by the lens combination given in the Fig 9 20 FIGURE 9
9
583-586
9 20 FIGURE 9 20 Solution Image formed by the first lens 1 1 1 1 1 1 v u f − = 1 1 1 1 30 10 v − = − or v1 = 15 cm Rationalised 2023-24 Ray Optics and Optical Instruments 239 FIGURE 9
9
584-587
20 FIGURE 9 20 Solution Image formed by the first lens 1 1 1 1 1 1 v u f − = 1 1 1 1 30 10 v − = − or v1 = 15 cm Rationalised 2023-24 Ray Optics and Optical Instruments 239 FIGURE 9 21 A ray of light passing through a triangular glass prism
9
585-588
FIGURE 9 20 Solution Image formed by the first lens 1 1 1 1 1 1 v u f − = 1 1 1 1 30 10 v − = − or v1 = 15 cm Rationalised 2023-24 Ray Optics and Optical Instruments 239 FIGURE 9 21 A ray of light passing through a triangular glass prism EXAMPLE 9
9
586-589
20 Solution Image formed by the first lens 1 1 1 1 1 1 v u f − = 1 1 1 1 30 10 v − = − or v1 = 15 cm Rationalised 2023-24 Ray Optics and Optical Instruments 239 FIGURE 9 21 A ray of light passing through a triangular glass prism EXAMPLE 9 8 The image formed by the first lens serves as the object for the second
9
587-590
21 A ray of light passing through a triangular glass prism EXAMPLE 9 8 The image formed by the first lens serves as the object for the second This is at a distance of (15 – 5) cm = 10 cm to the right of the second lens
9
588-591
EXAMPLE 9 8 The image formed by the first lens serves as the object for the second This is at a distance of (15 – 5) cm = 10 cm to the right of the second lens Though the image is real, it serves as a virtual object for the second lens, which means that the rays appear to come from it for the second lens
9
589-592
8 The image formed by the first lens serves as the object for the second This is at a distance of (15 – 5) cm = 10 cm to the right of the second lens Though the image is real, it serves as a virtual object for the second lens, which means that the rays appear to come from it for the second lens 2 1 1 1 10 10 v − = − or v2 = ¥ The virtual image is formed at an infinite distance to the left of the second lens
9
590-593
This is at a distance of (15 – 5) cm = 10 cm to the right of the second lens Though the image is real, it serves as a virtual object for the second lens, which means that the rays appear to come from it for the second lens 2 1 1 1 10 10 v − = − or v2 = ¥ The virtual image is formed at an infinite distance to the left of the second lens This acts as an object for the third lens
9
591-594
Though the image is real, it serves as a virtual object for the second lens, which means that the rays appear to come from it for the second lens 2 1 1 1 10 10 v − = − or v2 = ¥ The virtual image is formed at an infinite distance to the left of the second lens This acts as an object for the third lens 3 3 3 1 1 1 v u f − = or 3 1 1 1 30 v = + ∞ or v3 = 30 cm The final image is formed 30 cm to the right of the third lens
9
592-595
2 1 1 1 10 10 v − = − or v2 = ¥ The virtual image is formed at an infinite distance to the left of the second lens This acts as an object for the third lens 3 3 3 1 1 1 v u f − = or 3 1 1 1 30 v = + ∞ or v3 = 30 cm The final image is formed 30 cm to the right of the third lens 9
9
593-596
This acts as an object for the third lens 3 3 3 1 1 1 v u f − = or 3 1 1 1 30 v = + ∞ or v3 = 30 cm The final image is formed 30 cm to the right of the third lens 9 6 REFRACTION THROUGH A PRISM Figure 9
9
594-597
3 3 3 1 1 1 v u f − = or 3 1 1 1 30 v = + ∞ or v3 = 30 cm The final image is formed 30 cm to the right of the third lens 9 6 REFRACTION THROUGH A PRISM Figure 9 21 shows the passage of light through a triangular prism ABC
9
595-598
9 6 REFRACTION THROUGH A PRISM Figure 9 21 shows the passage of light through a triangular prism ABC The angles of incidence and refraction at the first face AB are i and r1, while the angle of incidence (from glass to air) at the second face AC is r2 and the angle of refraction or emergence e
9
596-599
6 REFRACTION THROUGH A PRISM Figure 9 21 shows the passage of light through a triangular prism ABC The angles of incidence and refraction at the first face AB are i and r1, while the angle of incidence (from glass to air) at the second face AC is r2 and the angle of refraction or emergence e The angle between the emergent ray RS and the direction of the incident ray PQ is called the angle of deviation, d
9
597-600
21 shows the passage of light through a triangular prism ABC The angles of incidence and refraction at the first face AB are i and r1, while the angle of incidence (from glass to air) at the second face AC is r2 and the angle of refraction or emergence e The angle between the emergent ray RS and the direction of the incident ray PQ is called the angle of deviation, d In the quadrilateral AQNR, two of the angles (at the vertices Q and R) are right angles
9
598-601
The angles of incidence and refraction at the first face AB are i and r1, while the angle of incidence (from glass to air) at the second face AC is r2 and the angle of refraction or emergence e The angle between the emergent ray RS and the direction of the incident ray PQ is called the angle of deviation, d In the quadrilateral AQNR, two of the angles (at the vertices Q and R) are right angles Therefore, the sum of the other angles of the quadrilateral is 180°
9
599-602
The angle between the emergent ray RS and the direction of the incident ray PQ is called the angle of deviation, d In the quadrilateral AQNR, two of the angles (at the vertices Q and R) are right angles Therefore, the sum of the other angles of the quadrilateral is 180° ÐA + ÐQNR = 180° From the triangle QNR, r1 + r2 + ÐQNR = 180° Comparing these two equations, we get r1 + r2 = A (9
9
600-603
In the quadrilateral AQNR, two of the angles (at the vertices Q and R) are right angles Therefore, the sum of the other angles of the quadrilateral is 180° ÐA + ÐQNR = 180° From the triangle QNR, r1 + r2 + ÐQNR = 180° Comparing these two equations, we get r1 + r2 = A (9 34) The total deviation d is the sum of deviations at the two faces, d = (i – r1 ) + (e – r2 ) that is, d = i + e – A (9
9
601-604
Therefore, the sum of the other angles of the quadrilateral is 180° ÐA + ÐQNR = 180° From the triangle QNR, r1 + r2 + ÐQNR = 180° Comparing these two equations, we get r1 + r2 = A (9 34) The total deviation d is the sum of deviations at the two faces, d = (i – r1 ) + (e – r2 ) that is, d = i + e – A (9 35) Thus, the angle of deviation depends on the angle of incidence
9
602-605
ÐA + ÐQNR = 180° From the triangle QNR, r1 + r2 + ÐQNR = 180° Comparing these two equations, we get r1 + r2 = A (9 34) The total deviation d is the sum of deviations at the two faces, d = (i – r1 ) + (e – r2 ) that is, d = i + e – A (9 35) Thus, the angle of deviation depends on the angle of incidence A plot between the angle of deviation and angle of incidence is shown in Fig
9
603-606
34) The total deviation d is the sum of deviations at the two faces, d = (i – r1 ) + (e – r2 ) that is, d = i + e – A (9 35) Thus, the angle of deviation depends on the angle of incidence A plot between the angle of deviation and angle of incidence is shown in Fig 9
9
604-607
35) Thus, the angle of deviation depends on the angle of incidence A plot between the angle of deviation and angle of incidence is shown in Fig 9 22
9
605-608
A plot between the angle of deviation and angle of incidence is shown in Fig 9 22 You can see that, in general, any given value of d, except for i = e, corresponds to two values i and hence of e
9
606-609
9 22 You can see that, in general, any given value of d, except for i = e, corresponds to two values i and hence of e This, in fact, is expected from the symmetry of i and e in Eq
9
607-610
22 You can see that, in general, any given value of d, except for i = e, corresponds to two values i and hence of e This, in fact, is expected from the symmetry of i and e in Eq (9
9
608-611
You can see that, in general, any given value of d, except for i = e, corresponds to two values i and hence of e This, in fact, is expected from the symmetry of i and e in Eq (9 35), i
9
609-612
This, in fact, is expected from the symmetry of i and e in Eq (9 35), i e
9
610-613
(9 35), i e , d remains the same if i Rationalised 2023-24 Physics 240 and e are interchanged
9
611-614
35), i e , d remains the same if i Rationalised 2023-24 Physics 240 and e are interchanged Physically, this is related to the fact that the path of ray in Fig
9
612-615
e , d remains the same if i Rationalised 2023-24 Physics 240 and e are interchanged Physically, this is related to the fact that the path of ray in Fig 9
9
613-616
, d remains the same if i Rationalised 2023-24 Physics 240 and e are interchanged Physically, this is related to the fact that the path of ray in Fig 9 21 can be traced back, resulting in the same angle of deviation
9
614-617
Physically, this is related to the fact that the path of ray in Fig 9 21 can be traced back, resulting in the same angle of deviation At the minimum deviation Dm, the refracted ray inside the prism becomes parallel to its base
9
615-618
9 21 can be traced back, resulting in the same angle of deviation At the minimum deviation Dm, the refracted ray inside the prism becomes parallel to its base We have d = Dm, i = e which implies r1 = r2
9
616-619
21 can be traced back, resulting in the same angle of deviation At the minimum deviation Dm, the refracted ray inside the prism becomes parallel to its base We have d = Dm, i = e which implies r1 = r2 Equation (9
9
617-620
At the minimum deviation Dm, the refracted ray inside the prism becomes parallel to its base We have d = Dm, i = e which implies r1 = r2 Equation (9 34) gives 2r = A or r = 2 A (9
9
618-621
We have d = Dm, i = e which implies r1 = r2 Equation (9 34) gives 2r = A or r = 2 A (9 36) In the same way, Eq
9
619-622
Equation (9 34) gives 2r = A or r = 2 A (9 36) In the same way, Eq (9
9
620-623
34) gives 2r = A or r = 2 A (9 36) In the same way, Eq (9 35) gives Dm = 2i – A, or i = (A + Dm)/2 (9
9
621-624
36) In the same way, Eq (9 35) gives Dm = 2i – A, or i = (A + Dm)/2 (9 37) The refractive index of the prism is 2 21 1 sin[( )/2] sin[ /2] m A D n n n +A = = (9
9
622-625
(9 35) gives Dm = 2i – A, or i = (A + Dm)/2 (9 37) The refractive index of the prism is 2 21 1 sin[( )/2] sin[ /2] m A D n n n +A = = (9 38) The angles A and Dm can be measured experimentally
9
623-626
35) gives Dm = 2i – A, or i = (A + Dm)/2 (9 37) The refractive index of the prism is 2 21 1 sin[( )/2] sin[ /2] m A D n n n +A = = (9 38) The angles A and Dm can be measured experimentally Equation (9
9
624-627
37) The refractive index of the prism is 2 21 1 sin[( )/2] sin[ /2] m A D n n n +A = = (9 38) The angles A and Dm can be measured experimentally Equation (9 38) thus provides a method of determining refractive index of the material of the prism
9
625-628
38) The angles A and Dm can be measured experimentally Equation (9 38) thus provides a method of determining refractive index of the material of the prism For a small angle prism, i
9
626-629
Equation (9 38) thus provides a method of determining refractive index of the material of the prism For a small angle prism, i e
9
627-630
38) thus provides a method of determining refractive index of the material of the prism For a small angle prism, i e , a thin prism, Dm is also very small, and we get ( ) 21 /2 sin[( )/2] sin[ /2] /2 m m A D A D n A A + + = ≃ Dm = (n21–1)A It implies that, thin prisms do not deviate light much
9
628-631
For a small angle prism, i e , a thin prism, Dm is also very small, and we get ( ) 21 /2 sin[( )/2] sin[ /2] /2 m m A D A D n A A + + = ≃ Dm = (n21–1)A It implies that, thin prisms do not deviate light much 9
9
629-632
e , a thin prism, Dm is also very small, and we get ( ) 21 /2 sin[( )/2] sin[ /2] /2 m m A D A D n A A + + = ≃ Dm = (n21–1)A It implies that, thin prisms do not deviate light much 9 7 OPTICAL INSTRUMENTS A number of optical devices and instruments have been designed utilising reflecting and refracting properties of mirrors, lenses and prisms
9
630-633
, a thin prism, Dm is also very small, and we get ( ) 21 /2 sin[( )/2] sin[ /2] /2 m m A D A D n A A + + = ≃ Dm = (n21–1)A It implies that, thin prisms do not deviate light much 9 7 OPTICAL INSTRUMENTS A number of optical devices and instruments have been designed utilising reflecting and refracting properties of mirrors, lenses and prisms Periscope, kaleidoscope, binoculars, telescopes, microscopes are some examples of optical devices and instruments that are in common use
9
631-634
9 7 OPTICAL INSTRUMENTS A number of optical devices and instruments have been designed utilising reflecting and refracting properties of mirrors, lenses and prisms Periscope, kaleidoscope, binoculars, telescopes, microscopes are some examples of optical devices and instruments that are in common use Our eye is, of course, one of the most important optical device the nature has endowed us with
9
632-635
7 OPTICAL INSTRUMENTS A number of optical devices and instruments have been designed utilising reflecting and refracting properties of mirrors, lenses and prisms Periscope, kaleidoscope, binoculars, telescopes, microscopes are some examples of optical devices and instruments that are in common use Our eye is, of course, one of the most important optical device the nature has endowed us with We have already studied about the human eye in Class X
9
633-636
Periscope, kaleidoscope, binoculars, telescopes, microscopes are some examples of optical devices and instruments that are in common use Our eye is, of course, one of the most important optical device the nature has endowed us with We have already studied about the human eye in Class X We now go on to describe the principles of working of the microscope and the telescope
9
634-637
Our eye is, of course, one of the most important optical device the nature has endowed us with We have already studied about the human eye in Class X We now go on to describe the principles of working of the microscope and the telescope 9
9
635-638
We have already studied about the human eye in Class X We now go on to describe the principles of working of the microscope and the telescope 9 7
9
636-639
We now go on to describe the principles of working of the microscope and the telescope 9 7 1 The microscope A simple magnifier or microscope is a converging lens of small focal length (Fig
9
637-640
9 7 1 The microscope A simple magnifier or microscope is a converging lens of small focal length (Fig 9
9
638-641
7 1 The microscope A simple magnifier or microscope is a converging lens of small focal length (Fig 9 23)