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239-242
For example, turpentine and water Mass density of turpentine is less than that of water but its optical density is higher If n 21 is the refractive index of medium 2 with respect to medium 1 and n12 the refractive index of medium 1 with respect to medium 2, then it should be clear that 12 21 1 n =n (9 11) It also follows that if n 32 is the refractive index of medium 3 with respect to medium 2 then n 32 = n 31 × n 12, where n 31 is the refractive index of medium 3 with respect to medium 1
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240-243
Mass density of turpentine is less than that of water but its optical density is higher If n 21 is the refractive index of medium 2 with respect to medium 1 and n12 the refractive index of medium 1 with respect to medium 2, then it should be clear that 12 21 1 n =n (9 11) It also follows that if n 32 is the refractive index of medium 3 with respect to medium 2 then n 32 = n 31 × n 12, where n 31 is the refractive index of medium 3 with respect to medium 1 Some elementary results based on the laws of refraction follow immediately
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241-244
If n 21 is the refractive index of medium 2 with respect to medium 1 and n12 the refractive index of medium 1 with respect to medium 2, then it should be clear that 12 21 1 n =n (9 11) It also follows that if n 32 is the refractive index of medium 3 with respect to medium 2 then n 32 = n 31 × n 12, where n 31 is the refractive index of medium 3 with respect to medium 1 Some elementary results based on the laws of refraction follow immediately For a rectangular slab, refraction takes place at two interfaces (air- glass and glass-air)
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242-245
11) It also follows that if n 32 is the refractive index of medium 3 with respect to medium 2 then n 32 = n 31 × n 12, where n 31 is the refractive index of medium 3 with respect to medium 1 Some elementary results based on the laws of refraction follow immediately For a rectangular slab, refraction takes place at two interfaces (air- glass and glass-air) It is easily seen from Fig
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243-246
Some elementary results based on the laws of refraction follow immediately For a rectangular slab, refraction takes place at two interfaces (air- glass and glass-air) It is easily seen from Fig 9
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244-247
For a rectangular slab, refraction takes place at two interfaces (air- glass and glass-air) It is easily seen from Fig 9 9 that r2 = i1, i
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245-248
It is easily seen from Fig 9 9 that r2 = i1, i e
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246-249
9 9 that r2 = i1, i e , the emergent ray is parallel to the incident ray—there is no deviation, but it does suffer lateral displacement/shift with respect to the incident ray
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247-250
9 that r2 = i1, i e , the emergent ray is parallel to the incident ray—there is no deviation, but it does suffer lateral displacement/shift with respect to the incident ray Another familiar observation is that the bottom of a tank filled with water appears to be raised (Fig
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248-251
e , the emergent ray is parallel to the incident ray—there is no deviation, but it does suffer lateral displacement/shift with respect to the incident ray Another familiar observation is that the bottom of a tank filled with water appears to be raised (Fig 9
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249-252
, the emergent ray is parallel to the incident ray—there is no deviation, but it does suffer lateral displacement/shift with respect to the incident ray Another familiar observation is that the bottom of a tank filled with water appears to be raised (Fig 9 10)
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250-253
Another familiar observation is that the bottom of a tank filled with water appears to be raised (Fig 9 10) For viewing near the normal direction, it can be shown that the apparent depth (h1) is real depth (h 2) divided by the refractive index of the medium (water)
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251-254
9 10) For viewing near the normal direction, it can be shown that the apparent depth (h1) is real depth (h 2) divided by the refractive index of the medium (water) 9
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252-255
10) For viewing near the normal direction, it can be shown that the apparent depth (h1) is real depth (h 2) divided by the refractive index of the medium (water) 9 4 TOTAL INTERNAL REFLECTION When light travels from an optically denser medium to a rarer medium at the interface, it is partly reflected back into the same medium and partly refracted to the second medium
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253-256
For viewing near the normal direction, it can be shown that the apparent depth (h1) is real depth (h 2) divided by the refractive index of the medium (water) 9 4 TOTAL INTERNAL REFLECTION When light travels from an optically denser medium to a rarer medium at the interface, it is partly reflected back into the same medium and partly refracted to the second medium This reflection is called the internal reflection
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9 4 TOTAL INTERNAL REFLECTION When light travels from an optically denser medium to a rarer medium at the interface, it is partly reflected back into the same medium and partly refracted to the second medium This reflection is called the internal reflection When a ray of light enters from a denser medium to a rarer medium, it bends away from the normal, for example, the ray AO1 B in Fig
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255-258
4 TOTAL INTERNAL REFLECTION When light travels from an optically denser medium to a rarer medium at the interface, it is partly reflected back into the same medium and partly refracted to the second medium This reflection is called the internal reflection When a ray of light enters from a denser medium to a rarer medium, it bends away from the normal, for example, the ray AO1 B in Fig 9
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256-259
This reflection is called the internal reflection When a ray of light enters from a denser medium to a rarer medium, it bends away from the normal, for example, the ray AO1 B in Fig 9 11
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257-260
When a ray of light enters from a denser medium to a rarer medium, it bends away from the normal, for example, the ray AO1 B in Fig 9 11 The incident ray AO1 is partially reflected (O1C) and partially transmitted (O1B) or refracted, the angle of refraction (r) being larger than the angle of incidence (i)
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258-261
9 11 The incident ray AO1 is partially reflected (O1C) and partially transmitted (O1B) or refracted, the angle of refraction (r) being larger than the angle of incidence (i) As the angle of incidence increases, so does the angle of FIGURE 9
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259-262
11 The incident ray AO1 is partially reflected (O1C) and partially transmitted (O1B) or refracted, the angle of refraction (r) being larger than the angle of incidence (i) As the angle of incidence increases, so does the angle of FIGURE 9 10 Apparent depth for (a) normal, and (b) oblique viewing
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260-263
The incident ray AO1 is partially reflected (O1C) and partially transmitted (O1B) or refracted, the angle of refraction (r) being larger than the angle of incidence (i) As the angle of incidence increases, so does the angle of FIGURE 9 10 Apparent depth for (a) normal, and (b) oblique viewing FIGURE 9
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261-264
As the angle of incidence increases, so does the angle of FIGURE 9 10 Apparent depth for (a) normal, and (b) oblique viewing FIGURE 9 9 Lateral shift of a ray refracted through a parallel-sided slab
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262-265
10 Apparent depth for (a) normal, and (b) oblique viewing FIGURE 9 9 Lateral shift of a ray refracted through a parallel-sided slab Rationalised 2023-24 Physics 230 refraction, till for the ray AO3, the angle of refraction is p/2
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263-266
FIGURE 9 9 Lateral shift of a ray refracted through a parallel-sided slab Rationalised 2023-24 Physics 230 refraction, till for the ray AO3, the angle of refraction is p/2 The refracted ray is bent so much away from the normal that it grazes the surface at the interface between the two media
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264-267
9 Lateral shift of a ray refracted through a parallel-sided slab Rationalised 2023-24 Physics 230 refraction, till for the ray AO3, the angle of refraction is p/2 The refracted ray is bent so much away from the normal that it grazes the surface at the interface between the two media This is shown by the ray AO3 D in Fig
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265-268
Rationalised 2023-24 Physics 230 refraction, till for the ray AO3, the angle of refraction is p/2 The refracted ray is bent so much away from the normal that it grazes the surface at the interface between the two media This is shown by the ray AO3 D in Fig 9
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266-269
The refracted ray is bent so much away from the normal that it grazes the surface at the interface between the two media This is shown by the ray AO3 D in Fig 9 11
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267-270
This is shown by the ray AO3 D in Fig 9 11 If the angle of incidence is increased still further (e
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9 11 If the angle of incidence is increased still further (e g
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11 If the angle of incidence is increased still further (e g , the ray AO4), refraction is not possible, and the incident ray is totally reflected
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270-273
If the angle of incidence is increased still further (e g , the ray AO4), refraction is not possible, and the incident ray is totally reflected This is called total internal reflection
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271-274
g , the ray AO4), refraction is not possible, and the incident ray is totally reflected This is called total internal reflection When light gets reflected by a surface, normally some fraction of it gets transmitted
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272-275
, the ray AO4), refraction is not possible, and the incident ray is totally reflected This is called total internal reflection When light gets reflected by a surface, normally some fraction of it gets transmitted The reflected ray, therefore, is always less intense than the incident ray, howsoever smooth the reflecting surface may be
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This is called total internal reflection When light gets reflected by a surface, normally some fraction of it gets transmitted The reflected ray, therefore, is always less intense than the incident ray, howsoever smooth the reflecting surface may be In total internal reflection, on the other hand, no transmission of light takes place
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274-277
When light gets reflected by a surface, normally some fraction of it gets transmitted The reflected ray, therefore, is always less intense than the incident ray, howsoever smooth the reflecting surface may be In total internal reflection, on the other hand, no transmission of light takes place The angle of incidence corresponding to an angle of refraction 90°, say ÐAO3N, is called the critical angle (ic ) for the given pair of media
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275-278
The reflected ray, therefore, is always less intense than the incident ray, howsoever smooth the reflecting surface may be In total internal reflection, on the other hand, no transmission of light takes place The angle of incidence corresponding to an angle of refraction 90°, say ÐAO3N, is called the critical angle (ic ) for the given pair of media We see from Snell’s law [Eq
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276-279
In total internal reflection, on the other hand, no transmission of light takes place The angle of incidence corresponding to an angle of refraction 90°, say ÐAO3N, is called the critical angle (ic ) for the given pair of media We see from Snell’s law [Eq (9
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277-280
The angle of incidence corresponding to an angle of refraction 90°, say ÐAO3N, is called the critical angle (ic ) for the given pair of media We see from Snell’s law [Eq (9 10)] that if the relative refractive index of the refracting medium is less than one then, since the maximum value of sin r is unity, there is an upper limit to the value of sin i for which the law can be satisfied, that is, i = ic such that sin ic = n 21 (9
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278-281
We see from Snell’s law [Eq (9 10)] that if the relative refractive index of the refracting medium is less than one then, since the maximum value of sin r is unity, there is an upper limit to the value of sin i for which the law can be satisfied, that is, i = ic such that sin ic = n 21 (9 12) For values of i larger than ic, Snell’s law of refraction cannot be satisfied, and hence no refraction is possible
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(9 10)] that if the relative refractive index of the refracting medium is less than one then, since the maximum value of sin r is unity, there is an upper limit to the value of sin i for which the law can be satisfied, that is, i = ic such that sin ic = n 21 (9 12) For values of i larger than ic, Snell’s law of refraction cannot be satisfied, and hence no refraction is possible The refractive index of denser medium 1 with respect to rarer medium 2 will be n12 = 1/sinic
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280-283
10)] that if the relative refractive index of the refracting medium is less than one then, since the maximum value of sin r is unity, there is an upper limit to the value of sin i for which the law can be satisfied, that is, i = ic such that sin ic = n 21 (9 12) For values of i larger than ic, Snell’s law of refraction cannot be satisfied, and hence no refraction is possible The refractive index of denser medium 1 with respect to rarer medium 2 will be n12 = 1/sinic Some typical critical angles are listed in Table 9
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281-284
12) For values of i larger than ic, Snell’s law of refraction cannot be satisfied, and hence no refraction is possible The refractive index of denser medium 1 with respect to rarer medium 2 will be n12 = 1/sinic Some typical critical angles are listed in Table 9 1
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282-285
The refractive index of denser medium 1 with respect to rarer medium 2 will be n12 = 1/sinic Some typical critical angles are listed in Table 9 1 FIGURE 9
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283-286
Some typical critical angles are listed in Table 9 1 FIGURE 9 11 Refraction and internal reflection of rays from a point A in the denser medium (water) incident at different angles at the interface with a rarer medium (air)
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1 FIGURE 9 11 Refraction and internal reflection of rays from a point A in the denser medium (water) incident at different angles at the interface with a rarer medium (air) A demonstration for total internal reflection All optical phenomena can be demonstrated very easily with the use of a laser torch or pointer, which is easily available nowadays
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285-288
FIGURE 9 11 Refraction and internal reflection of rays from a point A in the denser medium (water) incident at different angles at the interface with a rarer medium (air) A demonstration for total internal reflection All optical phenomena can be demonstrated very easily with the use of a laser torch or pointer, which is easily available nowadays Take a glass beaker with clear water in it
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286-289
11 Refraction and internal reflection of rays from a point A in the denser medium (water) incident at different angles at the interface with a rarer medium (air) A demonstration for total internal reflection All optical phenomena can be demonstrated very easily with the use of a laser torch or pointer, which is easily available nowadays Take a glass beaker with clear water in it Add a few drops of milk or any other suspension to water and stir so that water becomes a little turbid
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287-290
A demonstration for total internal reflection All optical phenomena can be demonstrated very easily with the use of a laser torch or pointer, which is easily available nowadays Take a glass beaker with clear water in it Add a few drops of milk or any other suspension to water and stir so that water becomes a little turbid Take a laser pointer and shine its beam through the turbid water
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288-291
Take a glass beaker with clear water in it Add a few drops of milk or any other suspension to water and stir so that water becomes a little turbid Take a laser pointer and shine its beam through the turbid water You will find that the path of the beam inside the water shines brightly
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289-292
Add a few drops of milk or any other suspension to water and stir so that water becomes a little turbid Take a laser pointer and shine its beam through the turbid water You will find that the path of the beam inside the water shines brightly TABLE 9
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290-293
Take a laser pointer and shine its beam through the turbid water You will find that the path of the beam inside the water shines brightly TABLE 9 1 CRITICAL ANGLE OF SOME TRANSPARENT MEDIA WITH RESPECT TO AIR Substance medium Refractive index Critical angle Water 1
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291-294
You will find that the path of the beam inside the water shines brightly TABLE 9 1 CRITICAL ANGLE OF SOME TRANSPARENT MEDIA WITH RESPECT TO AIR Substance medium Refractive index Critical angle Water 1 33 48
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292-295
TABLE 9 1 CRITICAL ANGLE OF SOME TRANSPARENT MEDIA WITH RESPECT TO AIR Substance medium Refractive index Critical angle Water 1 33 48 75 Crown glass 1
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293-296
1 CRITICAL ANGLE OF SOME TRANSPARENT MEDIA WITH RESPECT TO AIR Substance medium Refractive index Critical angle Water 1 33 48 75 Crown glass 1 52 41
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294-297
33 48 75 Crown glass 1 52 41 14 Dense flint glass 1
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75 Crown glass 1 52 41 14 Dense flint glass 1 62 37
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296-299
52 41 14 Dense flint glass 1 62 37 31 Diamond 2
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14 Dense flint glass 1 62 37 31 Diamond 2 42 24
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62 37 31 Diamond 2 42 24 41 Rationalised 2023-24 Ray Optics and Optical Instruments 231 Shine the beam from below the beaker such that it strikes at the upper water surface at the other end
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31 Diamond 2 42 24 41 Rationalised 2023-24 Ray Optics and Optical Instruments 231 Shine the beam from below the beaker such that it strikes at the upper water surface at the other end Do you find that it undergoes partial reflection (which is seen as a spot on the table below) and partial refraction [which comes out in the air and is seen as a spot on the roof; Fig
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300-303
42 24 41 Rationalised 2023-24 Ray Optics and Optical Instruments 231 Shine the beam from below the beaker such that it strikes at the upper water surface at the other end Do you find that it undergoes partial reflection (which is seen as a spot on the table below) and partial refraction [which comes out in the air and is seen as a spot on the roof; Fig 9
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301-304
41 Rationalised 2023-24 Ray Optics and Optical Instruments 231 Shine the beam from below the beaker such that it strikes at the upper water surface at the other end Do you find that it undergoes partial reflection (which is seen as a spot on the table below) and partial refraction [which comes out in the air and is seen as a spot on the roof; Fig 9 12(a)]
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Do you find that it undergoes partial reflection (which is seen as a spot on the table below) and partial refraction [which comes out in the air and is seen as a spot on the roof; Fig 9 12(a)] Now direct the laser beam from one side of the beaker such that it strikes the upper surface of water more obliquely [Fig
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303-306
9 12(a)] Now direct the laser beam from one side of the beaker such that it strikes the upper surface of water more obliquely [Fig 9
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304-307
12(a)] Now direct the laser beam from one side of the beaker such that it strikes the upper surface of water more obliquely [Fig 9 12(b)]
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305-308
Now direct the laser beam from one side of the beaker such that it strikes the upper surface of water more obliquely [Fig 9 12(b)] Adjust the direction of laser beam until you find the angle for which the refraction above the water surface is totally absent and the beam is totally reflected back to water
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306-309
9 12(b)] Adjust the direction of laser beam until you find the angle for which the refraction above the water surface is totally absent and the beam is totally reflected back to water This is total internal reflection at its simplest
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307-310
12(b)] Adjust the direction of laser beam until you find the angle for which the refraction above the water surface is totally absent and the beam is totally reflected back to water This is total internal reflection at its simplest Pour this water in a long test tube and shine the laser light from top, as shown in Fig
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308-311
Adjust the direction of laser beam until you find the angle for which the refraction above the water surface is totally absent and the beam is totally reflected back to water This is total internal reflection at its simplest Pour this water in a long test tube and shine the laser light from top, as shown in Fig 9
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309-312
This is total internal reflection at its simplest Pour this water in a long test tube and shine the laser light from top, as shown in Fig 9 12(c)
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310-313
Pour this water in a long test tube and shine the laser light from top, as shown in Fig 9 12(c) Adjust the direction of the laser beam such that it is totally internally reflected every time it strikes the walls of the tube
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311-314
9 12(c) Adjust the direction of the laser beam such that it is totally internally reflected every time it strikes the walls of the tube This is similar to what happens in optical fibres
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12(c) Adjust the direction of the laser beam such that it is totally internally reflected every time it strikes the walls of the tube This is similar to what happens in optical fibres Take care not to look into the laser beam directly and not to point it at anybody’s face
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313-316
Adjust the direction of the laser beam such that it is totally internally reflected every time it strikes the walls of the tube This is similar to what happens in optical fibres Take care not to look into the laser beam directly and not to point it at anybody’s face 9
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314-317
This is similar to what happens in optical fibres Take care not to look into the laser beam directly and not to point it at anybody’s face 9 4
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315-318
Take care not to look into the laser beam directly and not to point it at anybody’s face 9 4 1 Total internal reflection in nature and its technelogical applications (i) Prism: Prisms designed to bend light by 90° or by 180° make use of total internal reflection [Fig
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316-319
9 4 1 Total internal reflection in nature and its technelogical applications (i) Prism: Prisms designed to bend light by 90° or by 180° make use of total internal reflection [Fig 9
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317-320
4 1 Total internal reflection in nature and its technelogical applications (i) Prism: Prisms designed to bend light by 90° or by 180° make use of total internal reflection [Fig 9 13(a) and (b)]
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318-321
1 Total internal reflection in nature and its technelogical applications (i) Prism: Prisms designed to bend light by 90° or by 180° make use of total internal reflection [Fig 9 13(a) and (b)] Such a prism is also used to invert images without chxanging their size [Fig
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319-322
9 13(a) and (b)] Such a prism is also used to invert images without chxanging their size [Fig 9
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320-323
13(a) and (b)] Such a prism is also used to invert images without chxanging their size [Fig 9 13(c)]
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321-324
Such a prism is also used to invert images without chxanging their size [Fig 9 13(c)] In the first two cases, the critical angle ic for the material of the prism must be less than 45°
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322-325
9 13(c)] In the first two cases, the critical angle ic for the material of the prism must be less than 45° We see from Table 9
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323-326
13(c)] In the first two cases, the critical angle ic for the material of the prism must be less than 45° We see from Table 9 1 that this is true for both crown glass and dense flint glass
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324-327
In the first two cases, the critical angle ic for the material of the prism must be less than 45° We see from Table 9 1 that this is true for both crown glass and dense flint glass (ii) Optical fibres: Nowadays optical fibres are extensively used for transmitting audio and video signals through long distances
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325-328
We see from Table 9 1 that this is true for both crown glass and dense flint glass (ii) Optical fibres: Nowadays optical fibres are extensively used for transmitting audio and video signals through long distances Optical fibres too make use of the phenomenon of total internal reflection
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326-329
1 that this is true for both crown glass and dense flint glass (ii) Optical fibres: Nowadays optical fibres are extensively used for transmitting audio and video signals through long distances Optical fibres too make use of the phenomenon of total internal reflection Optical fibres are fabricated with high quality composite glass/quartz fibres
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327-330
(ii) Optical fibres: Nowadays optical fibres are extensively used for transmitting audio and video signals through long distances Optical fibres too make use of the phenomenon of total internal reflection Optical fibres are fabricated with high quality composite glass/quartz fibres Each fibre consists of a core and cladding
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328-331
Optical fibres too make use of the phenomenon of total internal reflection Optical fibres are fabricated with high quality composite glass/quartz fibres Each fibre consists of a core and cladding The refractive index of the material of the core is higher than that of the cladding
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329-332
Optical fibres are fabricated with high quality composite glass/quartz fibres Each fibre consists of a core and cladding The refractive index of the material of the core is higher than that of the cladding When a signal in the form of light is directed at one end of the fibre at a suitable angle, it undergoes repeated total internal reflections along the length of the fibre and finally comes out at the other end (Fig
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330-333
Each fibre consists of a core and cladding The refractive index of the material of the core is higher than that of the cladding When a signal in the form of light is directed at one end of the fibre at a suitable angle, it undergoes repeated total internal reflections along the length of the fibre and finally comes out at the other end (Fig 9
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331-334
The refractive index of the material of the core is higher than that of the cladding When a signal in the form of light is directed at one end of the fibre at a suitable angle, it undergoes repeated total internal reflections along the length of the fibre and finally comes out at the other end (Fig 9 14)
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332-335
When a signal in the form of light is directed at one end of the fibre at a suitable angle, it undergoes repeated total internal reflections along the length of the fibre and finally comes out at the other end (Fig 9 14) Since light undergoes total internal reflection at each stage, there is no appreciable loss in the intensity of the light signal
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333-336
9 14) Since light undergoes total internal reflection at each stage, there is no appreciable loss in the intensity of the light signal Optical fibres are fabricated such that light reflected at one side of inner surface strikes the other at an angle larger than the critical angle
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334-337
14) Since light undergoes total internal reflection at each stage, there is no appreciable loss in the intensity of the light signal Optical fibres are fabricated such that light reflected at one side of inner surface strikes the other at an angle larger than the critical angle Even if the fibre is bent, light can easily travel along its length
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335-338
Since light undergoes total internal reflection at each stage, there is no appreciable loss in the intensity of the light signal Optical fibres are fabricated such that light reflected at one side of inner surface strikes the other at an angle larger than the critical angle Even if the fibre is bent, light can easily travel along its length Thus, an optical fibre can be used to act as an optical pipe
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336-339
Optical fibres are fabricated such that light reflected at one side of inner surface strikes the other at an angle larger than the critical angle Even if the fibre is bent, light can easily travel along its length Thus, an optical fibre can be used to act as an optical pipe A bundle of optical fibres can be put to several uses
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337-340
Even if the fibre is bent, light can easily travel along its length Thus, an optical fibre can be used to act as an optical pipe A bundle of optical fibres can be put to several uses Optical fibres are extensively used for transmitting and receiving FIGURE 9
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338-341
Thus, an optical fibre can be used to act as an optical pipe A bundle of optical fibres can be put to several uses Optical fibres are extensively used for transmitting and receiving FIGURE 9 12 Observing total internal reflection in water with a laser beam (refraction due to glass of beaker neglected being very thin)