Page 1 [1] (Wave & Ray Optics) 1. In Youngâ€™s double slit experiment if the slit widths are in the ratio 1 : 9, the ratio of the intensity at minima to that at maxima will be (a) 1 (b) 1/9 (c) 1/4 (d) 1/3 2. Which of the following statements are true for light waves but not for sound waves ? (i) the speed of wave is greater in vacuum than in a medium (ii) waves of different frequencies travels with different speeds in a medium (iii) Waves travel with different speeds in different media. Choose your answer according to the code given below : (a) (i) and (ii) (b) (i) and (iii) (c) (ii) and (iii) (d) (i), (ii) and (iii) 3. For sustained interference we need two sources which emit radiation : (a) with same intensity (b) with same amplitude (c) having constant phase difference (d) in a narrow beam. 4. The intensity of the light emerging from the two slits in Youngâ€™s experiment is in the ratio 1 to 4. The intensity of the minimum to the consecutive maximum will be in the ratio of : (a) 1 : 2 (b) 1 : 4 (c) 1: 9 (d) none of these 5. A thin film is viewed in white light. The colour of the film seen at a particular point depends upon: (a) width of the source (b) distance of the source (c) location of the observer (d) none of these 6. In Youngâ€™s double slit experiment the 7 th maximum with wavelength ? 1 is at a distance d 1 and that with wavelength ? 2 is at distance d 2 . Then d 1 /d 2 = (a) ? 1 / ? 2 (b) ? 2 / ? 1 (c) ? 2 1 / ? 2 2 (d) ? 2 2 / ? 2 1 7. A light of 6000 Å is used to produce interference pattern. The observed fringe width is 0.12 mm. The angle between two interfering wave trains is (a) 2 x 10 â€“3 radian (b)3 x 10 â€“3 radian (c) 4x 10 â€“3 radian (d) 5x 10 â€“3 radian. 8. In a biprism experiment by using light of wavelength 5000 Å, 5 mm wide fringes are obtained on a screen 1.0 m away from the coherent sources. The separation between the two coherent sources is (a) 1.0mm (b) 0.1mm (c) 0.05mm (d) 0.01mm 9. When the light is incident at the plarising angle, which of the following is completely polarised ? ? (a) Refracted light (b) Reflected light (c) both reflected as well as refracted (d) neither reflected nor refracted light 10. In Youngâ€™s double slit experiment, if the widths of the slit are in the ratio 4 : 9, ratio of intensity of maxima to intensity of minima will be (a) 25:1 (b) 9:4 (c) 3:2 (d) 81:16. 11. Doppler shift for the light of wavelength 6000Å emitted from the sun is 0.04Å. If radius of the sun is 7 x 10 8 m then time period of rotation of the sun will be (a) 30days (b) 365 days (c) 24 hours (d) 25 days. 12. In youngâ€™s double slit experiment a maximum is obtained when the path difference between the interfering waves is (Given that n = 1, 2, 3, 4â€¦.) (a) n 2 ? (b) n ? (c) (2n + 1) 2 ? (d) other than that given above 13. A piano-convex lens when silvered on the plane side behaves like a concave mirror of focal length 30 cm. When silvered on convex side, it behaves like a concave mirror of focal length 10 cm. The refractive index of material is (a) 3.0 (b) 2.0 (c) 2.5 (d) 1.5 14. Fig. shows the path of ray through an equiangular glass prism. It is incident on face AC at the critical angle for glass air interface. The angle of deviation of ray is 108°. Find the refractive index of glass prism. (a) 1.01 (b) 2.02 (c) 1.45 (d) 1.72 Page 2 [1] (Wave & Ray Optics) 1. In Youngâ€™s double slit experiment if the slit widths are in the ratio 1 : 9, the ratio of the intensity at minima to that at maxima will be (a) 1 (b) 1/9 (c) 1/4 (d) 1/3 2. Which of the following statements are true for light waves but not for sound waves ? (i) the speed of wave is greater in vacuum than in a medium (ii) waves of different frequencies travels with different speeds in a medium (iii) Waves travel with different speeds in different media. Choose your answer according to the code given below : (a) (i) and (ii) (b) (i) and (iii) (c) (ii) and (iii) (d) (i), (ii) and (iii) 3. For sustained interference we need two sources which emit radiation : (a) with same intensity (b) with same amplitude (c) having constant phase difference (d) in a narrow beam. 4. The intensity of the light emerging from the two slits in Youngâ€™s experiment is in the ratio 1 to 4. The intensity of the minimum to the consecutive maximum will be in the ratio of : (a) 1 : 2 (b) 1 : 4 (c) 1: 9 (d) none of these 5. A thin film is viewed in white light. The colour of the film seen at a particular point depends upon: (a) width of the source (b) distance of the source (c) location of the observer (d) none of these 6. In Youngâ€™s double slit experiment the 7 th maximum with wavelength ? 1 is at a distance d 1 and that with wavelength ? 2 is at distance d 2 . Then d 1 /d 2 = (a) ? 1 / ? 2 (b) ? 2 / ? 1 (c) ? 2 1 / ? 2 2 (d) ? 2 2 / ? 2 1 7. A light of 6000 Å is used to produce interference pattern. The observed fringe width is 0.12 mm. The angle between two interfering wave trains is (a) 2 x 10 â€“3 radian (b)3 x 10 â€“3 radian (c) 4x 10 â€“3 radian (d) 5x 10 â€“3 radian. 8. In a biprism experiment by using light of wavelength 5000 Å, 5 mm wide fringes are obtained on a screen 1.0 m away from the coherent sources. The separation between the two coherent sources is (a) 1.0mm (b) 0.1mm (c) 0.05mm (d) 0.01mm 9. When the light is incident at the plarising angle, which of the following is completely polarised ? ? (a) Refracted light (b) Reflected light (c) both reflected as well as refracted (d) neither reflected nor refracted light 10. In Youngâ€™s double slit experiment, if the widths of the slit are in the ratio 4 : 9, ratio of intensity of maxima to intensity of minima will be (a) 25:1 (b) 9:4 (c) 3:2 (d) 81:16. 11. Doppler shift for the light of wavelength 6000Å emitted from the sun is 0.04Å. If radius of the sun is 7 x 10 8 m then time period of rotation of the sun will be (a) 30days (b) 365 days (c) 24 hours (d) 25 days. 12. In youngâ€™s double slit experiment a maximum is obtained when the path difference between the interfering waves is (Given that n = 1, 2, 3, 4â€¦.) (a) n 2 ? (b) n ? (c) (2n + 1) 2 ? (d) other than that given above 13. A piano-convex lens when silvered on the plane side behaves like a concave mirror of focal length 30 cm. When silvered on convex side, it behaves like a concave mirror of focal length 10 cm. The refractive index of material is (a) 3.0 (b) 2.0 (c) 2.5 (d) 1.5 14. Fig. shows the path of ray through an equiangular glass prism. It is incident on face AC at the critical angle for glass air interface. The angle of deviation of ray is 108°. Find the refractive index of glass prism. (a) 1.01 (b) 2.02 (c) 1.45 (d) 1.72 [2] 15. A thin prism of angle 5° is placed at a distance of 10 cm from the object. What is distance of image from the object? (a) 0.25 cm (b) 0.43 cm (c) 0.52 cm (d) 0.61 cm 16. The refractive index of the material of equilateral prism is 3 . The angle of minimum deviation for the prism is (a) 30° (b) 41° (c) 49° (d) 60°. 17. A light bulb is placed between two plane mirrors inclined at an angle of 60 °. The number of images formed are : (a) 6 (b) 2 (c) 5 (d) 4 18. What causes changes in the colours of the thin soap or oil films for the given beam of light ? (a) angle of incidence (b) angle of reflection (c) thickness of the film (d) none of these 19. Instead of using two slits as in Youngâ€™s experiment, if we use two separate but identical sodium lamps, which of the following will occur ? (a) General illumination (b) Widely separate interference (c) Very bright maximum (d) Very dark minimum 20. In Fresnelâ€™s biprism experiment, bands of width 0.185 mm are observed at a distance one meter from the slit. The image of the coherent sources is then produced at the same distance from the slit by placing a convex lens at 30 cm from the slit. The images are found to be separated by a distance of 0.70 cm. The wavelength of the light used is (a) 1295Å (b) 5550Å (c) 6000Å (d) 6500 Å 21. If two mirrors are kept at 60 ° to each other, then the number of images formed by them is (a) 5 (b) 6 (c) 7 (d) 8. 22. A light source approaches the observer with velocity 0.5c. Doppler shift for light of wavelength 5500 Å is (a) 616 Å (b) 1833 Å (c) 5500 Å (d) 6160 Å 23. On introducing a thin mica sheet of thickness 2 x 10 â€“6 m and refractive index 1.5 in the path of one of the waves, central bright maxima shifts by n fringes. Wavelength of the wave used is 5000 Å, then n is (a) 1 (b) 2 (c) 5 (d) 10. 24. The focal length of a lens in a camera is marked Æ’: 2.8 is 8 cm. What is diameter of lens? (a) 1.4 cm (b) 2.8 cm (c) 3.2 cm (d) 4.0 cm 25. A plano-convex lens fits exactly into a plano- concave lens. Their plane surfaces are parallel to each other. If the lenses are made of different materials, what is focal length of combination ? Given Æ’ 1 = focal length of piano-concave lens Æ’ 2 = focal length of piano-convex lens µ 1 = ref. index of material of piano-concave lens µ 2 = ref. index of material of piano convex lens. (a) R 1 2 µ - µ (b) 1 2 R µ - µ (c) R 2 1 µ µ (d) R 1 2 µ µ In every question a statement of ASSERTION is followed by a statement of REASON. Mark the correct answer out of the following choices: (a) If both ASSERTION and REASON are true and reason is the correct explanation of the assertion. (b) If both ASSERTION and REASON are true but reason is not the correct explanation of the assertion. (c) If ASSERTION is true but REASON is false. (d) If ASSERTION is false but REASON is true. 26. Assertion: According to dual theory, light has a particle and wave nature at the same time. Reason: Any, particle or wave nature of light may be needed to explain a particular phenomenon. 27. Assertion: Light emerging from a convex lens when a point source is placed at its focus produces a plane wavefront. Page 3 [1] (Wave & Ray Optics) 1. In Youngâ€™s double slit experiment if the slit widths are in the ratio 1 : 9, the ratio of the intensity at minima to that at maxima will be (a) 1 (b) 1/9 (c) 1/4 (d) 1/3 2. Which of the following statements are true for light waves but not for sound waves ? (i) the speed of wave is greater in vacuum than in a medium (ii) waves of different frequencies travels with different speeds in a medium (iii) Waves travel with different speeds in different media. Choose your answer according to the code given below : (a) (i) and (ii) (b) (i) and (iii) (c) (ii) and (iii) (d) (i), (ii) and (iii) 3. For sustained interference we need two sources which emit radiation : (a) with same intensity (b) with same amplitude (c) having constant phase difference (d) in a narrow beam. 4. The intensity of the light emerging from the two slits in Youngâ€™s experiment is in the ratio 1 to 4. The intensity of the minimum to the consecutive maximum will be in the ratio of : (a) 1 : 2 (b) 1 : 4 (c) 1: 9 (d) none of these 5. A thin film is viewed in white light. The colour of the film seen at a particular point depends upon: (a) width of the source (b) distance of the source (c) location of the observer (d) none of these 6. In Youngâ€™s double slit experiment the 7 th maximum with wavelength ? 1 is at a distance d 1 and that with wavelength ? 2 is at distance d 2 . Then d 1 /d 2 = (a) ? 1 / ? 2 (b) ? 2 / ? 1 (c) ? 2 1 / ? 2 2 (d) ? 2 2 / ? 2 1 7. A light of 6000 Å is used to produce interference pattern. The observed fringe width is 0.12 mm. The angle between two interfering wave trains is (a) 2 x 10 â€“3 radian (b)3 x 10 â€“3 radian (c) 4x 10 â€“3 radian (d) 5x 10 â€“3 radian. 8. In a biprism experiment by using light of wavelength 5000 Å, 5 mm wide fringes are obtained on a screen 1.0 m away from the coherent sources. The separation between the two coherent sources is (a) 1.0mm (b) 0.1mm (c) 0.05mm (d) 0.01mm 9. When the light is incident at the plarising angle, which of the following is completely polarised ? ? (a) Refracted light (b) Reflected light (c) both reflected as well as refracted (d) neither reflected nor refracted light 10. In Youngâ€™s double slit experiment, if the widths of the slit are in the ratio 4 : 9, ratio of intensity of maxima to intensity of minima will be (a) 25:1 (b) 9:4 (c) 3:2 (d) 81:16. 11. Doppler shift for the light of wavelength 6000Å emitted from the sun is 0.04Å. If radius of the sun is 7 x 10 8 m then time period of rotation of the sun will be (a) 30days (b) 365 days (c) 24 hours (d) 25 days. 12. In youngâ€™s double slit experiment a maximum is obtained when the path difference between the interfering waves is (Given that n = 1, 2, 3, 4â€¦.) (a) n 2 ? (b) n ? (c) (2n + 1) 2 ? (d) other than that given above 13. A piano-convex lens when silvered on the plane side behaves like a concave mirror of focal length 30 cm. When silvered on convex side, it behaves like a concave mirror of focal length 10 cm. The refractive index of material is (a) 3.0 (b) 2.0 (c) 2.5 (d) 1.5 14. Fig. shows the path of ray through an equiangular glass prism. It is incident on face AC at the critical angle for glass air interface. The angle of deviation of ray is 108°. Find the refractive index of glass prism. (a) 1.01 (b) 2.02 (c) 1.45 (d) 1.72 [2] 15. A thin prism of angle 5° is placed at a distance of 10 cm from the object. What is distance of image from the object? (a) 0.25 cm (b) 0.43 cm (c) 0.52 cm (d) 0.61 cm 16. The refractive index of the material of equilateral prism is 3 . The angle of minimum deviation for the prism is (a) 30° (b) 41° (c) 49° (d) 60°. 17. A light bulb is placed between two plane mirrors inclined at an angle of 60 °. The number of images formed are : (a) 6 (b) 2 (c) 5 (d) 4 18. What causes changes in the colours of the thin soap or oil films for the given beam of light ? (a) angle of incidence (b) angle of reflection (c) thickness of the film (d) none of these 19. Instead of using two slits as in Youngâ€™s experiment, if we use two separate but identical sodium lamps, which of the following will occur ? (a) General illumination (b) Widely separate interference (c) Very bright maximum (d) Very dark minimum 20. In Fresnelâ€™s biprism experiment, bands of width 0.185 mm are observed at a distance one meter from the slit. The image of the coherent sources is then produced at the same distance from the slit by placing a convex lens at 30 cm from the slit. The images are found to be separated by a distance of 0.70 cm. The wavelength of the light used is (a) 1295Å (b) 5550Å (c) 6000Å (d) 6500 Å 21. If two mirrors are kept at 60 ° to each other, then the number of images formed by them is (a) 5 (b) 6 (c) 7 (d) 8. 22. A light source approaches the observer with velocity 0.5c. Doppler shift for light of wavelength 5500 Å is (a) 616 Å (b) 1833 Å (c) 5500 Å (d) 6160 Å 23. On introducing a thin mica sheet of thickness 2 x 10 â€“6 m and refractive index 1.5 in the path of one of the waves, central bright maxima shifts by n fringes. Wavelength of the wave used is 5000 Å, then n is (a) 1 (b) 2 (c) 5 (d) 10. 24. The focal length of a lens in a camera is marked Æ’: 2.8 is 8 cm. What is diameter of lens? (a) 1.4 cm (b) 2.8 cm (c) 3.2 cm (d) 4.0 cm 25. A plano-convex lens fits exactly into a plano- concave lens. Their plane surfaces are parallel to each other. If the lenses are made of different materials, what is focal length of combination ? Given Æ’ 1 = focal length of piano-concave lens Æ’ 2 = focal length of piano-convex lens µ 1 = ref. index of material of piano-concave lens µ 2 = ref. index of material of piano convex lens. (a) R 1 2 µ - µ (b) 1 2 R µ - µ (c) R 2 1 µ µ (d) R 1 2 µ µ In every question a statement of ASSERTION is followed by a statement of REASON. Mark the correct answer out of the following choices: (a) If both ASSERTION and REASON are true and reason is the correct explanation of the assertion. (b) If both ASSERTION and REASON are true but reason is not the correct explanation of the assertion. (c) If ASSERTION is true but REASON is false. (d) If ASSERTION is false but REASON is true. 26. Assertion: According to dual theory, light has a particle and wave nature at the same time. Reason: Any, particle or wave nature of light may be needed to explain a particular phenomenon. 27. Assertion: Light emerging from a convex lens when a point source is placed at its focus produces a plane wavefront. [3] Reason: A spherical wavefront on entering an inhomogenous anisotropic medium becomes a plane wavefront. 28. Assertion: In Youngâ€™s double slit experiment if the point on the screen directly opposite to a slit is dark then the wavelength of the source is proportional to square of the distance between the slits. Reason: A minima is obtained when the path difference is (2n + 1) 2 ? and the phase difference is (2n + 1) p. 29. Assertion: A narrow pulse of light, through a medium retains its shape as it travels through the medium. Reason: A narrow pulse of light is made of harmonic waves with a large range of wavelengths. 30. Assertion: One of the two polaroids crossed to each other is rotated through 30 °. Only 1/8th of the incident unpolarised light passes through the combination. Reason: The amount of light going through the Polaroid is determined by Malusâ€™ law. ANSWER KEY 1 C 6 A 11 D 16 D 21 A 26 D 2 A 7 D 12 B 17 C 22 B 27 C 3 C 8 B 13 D 18 C 23 B 28 A 4 C 9 B 14 C 19 A 24 B 29 D 5 C 10 A 15 B 20 B 25 B 30 A SOLUTIONS 1. Amplitude of the superimposing waves are A 1 /A 2 = (1/9) 1/2 = 1/3 4 1 ) A A ( ) A A ( I I 2 2 1 2 2 1 ima max ima min = + - = 2. Speed of sound in vacuum is zero. Also there is no dispersion of sound wave. So both (i) and (ii) are not valid for sound waves. 3. (c) 4. Amplitude are in the ratio 1 : 2. Hence amplitude at minimum will be 1 and that at maximum will be 3. 5. (c) 6. 7 ß = 7 D ? 1 /d = d 1 and 7 ß 2 = 7D ?/d = d 2 Hence ? 1 / ? 2 = d 1 /d 2 7. Here ß = d D ? Angle ? between two waves train is ? = ß ? = D d or ? = 3 10 10 12 . 0 10 6000 - - × × \ 8. use ß = d D ? 9. (b) 10. 4 9 I I W W 2 1 2 1 = = ? 4 9 a a 2 2 2 1 = 2 3 a a 2 1 = a max = a 1 + a 2 a min = a 1 - a 2 ? min max I I = 1 25 ) a a ( ) a a ( 2 1 2 1 = - + 11. Dopplerâ€™s shift is given by ? ? = ? ? ? ? ? ? ? ? = ? c . R c v ? = T 2 p ? R. ? ? ? ? ? ? p T 2 . ? = ? d c T = days 25 c / . dr 2 . R = ? p 12. (b) 13. Focal length of plano -convex lens f 1 = 1 R - µ â€¦(1) (i) Focal length equivalent concave mirror, when one side of lens is silvered m m l f 1 R ) 1 ( 2 f 1 f 2 F 1 + - µ = + = â€¦â€¦..(2) (ii) When plane side is silvered, then f m = 8 , so eqn. (2) gives 8 + - µ = 1 R ) 1 ( 2 F 1 1 R ) 1 ( 2 30 1 - µ = (iii) When convex side of its silvered f m = 2 R , so eqn. (2) gives R 2 R 2 R ) 1 ( 2 F 1 2 µ = + - µ = R 2 10 1 µ = â€¦(4). Dividing (3) by (4) µ - µ = 1 30 10 ? µ = 3 ( µ - 1) or µ = 1.5 14. Let i be angle of incidence at Q. Then angle of refraction at Q is 90 ° - (180 ° - A - 90 ° + C) = A - C. Angle of incidence at S is also (A - C), so angle Page 4 [1] (Wave & Ray Optics) 1. In Youngâ€™s double slit experiment if the slit widths are in the ratio 1 : 9, the ratio of the intensity at minima to that at maxima will be (a) 1 (b) 1/9 (c) 1/4 (d) 1/3 2. Which of the following statements are true for light waves but not for sound waves ? (i) the speed of wave is greater in vacuum than in a medium (ii) waves of different frequencies travels with different speeds in a medium (iii) Waves travel with different speeds in different media. Choose your answer according to the code given below : (a) (i) and (ii) (b) (i) and (iii) (c) (ii) and (iii) (d) (i), (ii) and (iii) 3. For sustained interference we need two sources which emit radiation : (a) with same intensity (b) with same amplitude (c) having constant phase difference (d) in a narrow beam. 4. The intensity of the light emerging from the two slits in Youngâ€™s experiment is in the ratio 1 to 4. The intensity of the minimum to the consecutive maximum will be in the ratio of : (a) 1 : 2 (b) 1 : 4 (c) 1: 9 (d) none of these 5. A thin film is viewed in white light. The colour of the film seen at a particular point depends upon: (a) width of the source (b) distance of the source (c) location of the observer (d) none of these 6. In Youngâ€™s double slit experiment the 7 th maximum with wavelength ? 1 is at a distance d 1 and that with wavelength ? 2 is at distance d 2 . Then d 1 /d 2 = (a) ? 1 / ? 2 (b) ? 2 / ? 1 (c) ? 2 1 / ? 2 2 (d) ? 2 2 / ? 2 1 7. A light of 6000 Å is used to produce interference pattern. The observed fringe width is 0.12 mm. The angle between two interfering wave trains is (a) 2 x 10 â€“3 radian (b)3 x 10 â€“3 radian (c) 4x 10 â€“3 radian (d) 5x 10 â€“3 radian. 8. In a biprism experiment by using light of wavelength 5000 Å, 5 mm wide fringes are obtained on a screen 1.0 m away from the coherent sources. The separation between the two coherent sources is (a) 1.0mm (b) 0.1mm (c) 0.05mm (d) 0.01mm 9. When the light is incident at the plarising angle, which of the following is completely polarised ? ? (a) Refracted light (b) Reflected light (c) both reflected as well as refracted (d) neither reflected nor refracted light 10. In Youngâ€™s double slit experiment, if the widths of the slit are in the ratio 4 : 9, ratio of intensity of maxima to intensity of minima will be (a) 25:1 (b) 9:4 (c) 3:2 (d) 81:16. 11. Doppler shift for the light of wavelength 6000Å emitted from the sun is 0.04Å. If radius of the sun is 7 x 10 8 m then time period of rotation of the sun will be (a) 30days (b) 365 days (c) 24 hours (d) 25 days. 12. In youngâ€™s double slit experiment a maximum is obtained when the path difference between the interfering waves is (Given that n = 1, 2, 3, 4â€¦.) (a) n 2 ? (b) n ? (c) (2n + 1) 2 ? (d) other than that given above 13. A piano-convex lens when silvered on the plane side behaves like a concave mirror of focal length 30 cm. When silvered on convex side, it behaves like a concave mirror of focal length 10 cm. The refractive index of material is (a) 3.0 (b) 2.0 (c) 2.5 (d) 1.5 14. Fig. shows the path of ray through an equiangular glass prism. It is incident on face AC at the critical angle for glass air interface. The angle of deviation of ray is 108°. Find the refractive index of glass prism. (a) 1.01 (b) 2.02 (c) 1.45 (d) 1.72 [2] 15. A thin prism of angle 5° is placed at a distance of 10 cm from the object. What is distance of image from the object? (a) 0.25 cm (b) 0.43 cm (c) 0.52 cm (d) 0.61 cm 16. The refractive index of the material of equilateral prism is 3 . The angle of minimum deviation for the prism is (a) 30° (b) 41° (c) 49° (d) 60°. 17. A light bulb is placed between two plane mirrors inclined at an angle of 60 °. The number of images formed are : (a) 6 (b) 2 (c) 5 (d) 4 18. What causes changes in the colours of the thin soap or oil films for the given beam of light ? (a) angle of incidence (b) angle of reflection (c) thickness of the film (d) none of these 19. Instead of using two slits as in Youngâ€™s experiment, if we use two separate but identical sodium lamps, which of the following will occur ? (a) General illumination (b) Widely separate interference (c) Very bright maximum (d) Very dark minimum 20. In Fresnelâ€™s biprism experiment, bands of width 0.185 mm are observed at a distance one meter from the slit. The image of the coherent sources is then produced at the same distance from the slit by placing a convex lens at 30 cm from the slit. The images are found to be separated by a distance of 0.70 cm. The wavelength of the light used is (a) 1295Å (b) 5550Å (c) 6000Å (d) 6500 Å 21. If two mirrors are kept at 60 ° to each other, then the number of images formed by them is (a) 5 (b) 6 (c) 7 (d) 8. 22. A light source approaches the observer with velocity 0.5c. Doppler shift for light of wavelength 5500 Å is (a) 616 Å (b) 1833 Å (c) 5500 Å (d) 6160 Å 23. On introducing a thin mica sheet of thickness 2 x 10 â€“6 m and refractive index 1.5 in the path of one of the waves, central bright maxima shifts by n fringes. Wavelength of the wave used is 5000 Å, then n is (a) 1 (b) 2 (c) 5 (d) 10. 24. The focal length of a lens in a camera is marked Æ’: 2.8 is 8 cm. What is diameter of lens? (a) 1.4 cm (b) 2.8 cm (c) 3.2 cm (d) 4.0 cm 25. A plano-convex lens fits exactly into a plano- concave lens. Their plane surfaces are parallel to each other. If the lenses are made of different materials, what is focal length of combination ? Given Æ’ 1 = focal length of piano-concave lens Æ’ 2 = focal length of piano-convex lens µ 1 = ref. index of material of piano-concave lens µ 2 = ref. index of material of piano convex lens. (a) R 1 2 µ - µ (b) 1 2 R µ - µ (c) R 2 1 µ µ (d) R 1 2 µ µ In every question a statement of ASSERTION is followed by a statement of REASON. Mark the correct answer out of the following choices: (a) If both ASSERTION and REASON are true and reason is the correct explanation of the assertion. (b) If both ASSERTION and REASON are true but reason is not the correct explanation of the assertion. (c) If ASSERTION is true but REASON is false. (d) If ASSERTION is false but REASON is true. 26. Assertion: According to dual theory, light has a particle and wave nature at the same time. Reason: Any, particle or wave nature of light may be needed to explain a particular phenomenon. 27. Assertion: Light emerging from a convex lens when a point source is placed at its focus produces a plane wavefront. [3] Reason: A spherical wavefront on entering an inhomogenous anisotropic medium becomes a plane wavefront. 28. Assertion: In Youngâ€™s double slit experiment if the point on the screen directly opposite to a slit is dark then the wavelength of the source is proportional to square of the distance between the slits. Reason: A minima is obtained when the path difference is (2n + 1) 2 ? and the phase difference is (2n + 1) p. 29. Assertion: A narrow pulse of light, through a medium retains its shape as it travels through the medium. Reason: A narrow pulse of light is made of harmonic waves with a large range of wavelengths. 30. Assertion: One of the two polaroids crossed to each other is rotated through 30 °. Only 1/8th of the incident unpolarised light passes through the combination. Reason: The amount of light going through the Polaroid is determined by Malusâ€™ law. ANSWER KEY 1 C 6 A 11 D 16 D 21 A 26 D 2 A 7 D 12 B 17 C 22 B 27 C 3 C 8 B 13 D 18 C 23 B 28 A 4 C 9 B 14 C 19 A 24 B 29 D 5 C 10 A 15 B 20 B 25 B 30 A SOLUTIONS 1. Amplitude of the superimposing waves are A 1 /A 2 = (1/9) 1/2 = 1/3 4 1 ) A A ( ) A A ( I I 2 2 1 2 2 1 ima max ima min = + - = 2. Speed of sound in vacuum is zero. Also there is no dispersion of sound wave. So both (i) and (ii) are not valid for sound waves. 3. (c) 4. Amplitude are in the ratio 1 : 2. Hence amplitude at minimum will be 1 and that at maximum will be 3. 5. (c) 6. 7 ß = 7 D ? 1 /d = d 1 and 7 ß 2 = 7D ?/d = d 2 Hence ? 1 / ? 2 = d 1 /d 2 7. Here ß = d D ? Angle ? between two waves train is ? = ß ? = D d or ? = 3 10 10 12 . 0 10 6000 - - × × \ 8. use ß = d D ? 9. (b) 10. 4 9 I I W W 2 1 2 1 = = ? 4 9 a a 2 2 2 1 = 2 3 a a 2 1 = a max = a 1 + a 2 a min = a 1 - a 2 ? min max I I = 1 25 ) a a ( ) a a ( 2 1 2 1 = - + 11. Dopplerâ€™s shift is given by ? ? = ? ? ? ? ? ? ? ? = ? c . R c v ? = T 2 p ? R. ? ? ? ? ? ? p T 2 . ? = ? d c T = days 25 c / . dr 2 . R = ? p 12. (b) 13. Focal length of plano -convex lens f 1 = 1 R - µ â€¦(1) (i) Focal length equivalent concave mirror, when one side of lens is silvered m m l f 1 R ) 1 ( 2 f 1 f 2 F 1 + - µ = + = â€¦â€¦..(2) (ii) When plane side is silvered, then f m = 8 , so eqn. (2) gives 8 + - µ = 1 R ) 1 ( 2 F 1 1 R ) 1 ( 2 30 1 - µ = (iii) When convex side of its silvered f m = 2 R , so eqn. (2) gives R 2 R 2 R ) 1 ( 2 F 1 2 µ = + - µ = R 2 10 1 µ = â€¦(4). Dividing (3) by (4) µ - µ = 1 30 10 ? µ = 3 ( µ - 1) or µ = 1.5 14. Let i be angle of incidence at Q. Then angle of refraction at Q is 90 ° - (180 ° - A - 90 ° + C) = A - C. Angle of incidence at S is also (A - C), so angle [4] of emergence at S is also i. Total deviation is algebraic sum of deviation at Q. R and S. 108 ° = i - (A - C) + 180 ° - 2C + i - (A -C) 2i - 2A + 180 ° = 2i - 120 ° + 180 ° or i = 24 ° µ = ) C 60 ( sin 24 sin r sin i sin - ° = After solving, µ = 1.45 15. D = ( µ - 1) A Distance of image from the object = OI = OE × D = µ × ( µ - 1) A ? OI = 10 (1.5 - 1) × cm 43 . 0 180 5 = ° × p 16. µ = 2 A sin 2 A sin r sin i sin d + = ° d + = 30 sin 2 A sin 3 , because A = 60 ° or sin ° = = d + 60 sin 2 3 2 A or A + d = 2 × 60 = 120 °. This gives d = 60 ° 17. Number of images N = 1 360 - ? . Where ? is in degrees. Here ? = 60 ° . Hence N = 5. 18. (c) 19. The superimposing waves will not be in constant phase. This leads to general illumination. 20. Here ß = 0.185 mm = 0.0185 cms D = 1.0 m = 100 cm u = = 30 cm ? v = 100 - 30 = 70 cm; Size of image, I = 0.70 cm Size of object, d = ? ? = ?. We know = v u image of size object of Size = 70 30 I d = d = cm 30 . 0 7 . 0 70 30 I 70 30 = × = × Now ? = 100 3 . 0 0185 . 0 D d × = ß = 555 × 10 - 7 cm = 5550 ? 21. (a) n = 60 360 -1 =5. 22. vâ€™ = ' c v c ? ? = + ? ?â€™ = 3667 c 5 . 0 c c 5500 v c c = + × = + ? Å ? ? ? = 95500 - 3667) = 1833 Å 23. shift is given by n ? = ( µ - 1) t. ? n = 2 t ) 1 ( = ? - µ 24. The meaning of mark f : 2.8 is that f is 2.8 times the aperture (diameter) of lens ? 8 = 2.8 × diameter or diameter = 8 . 2 cm 8 = 2.8 cm 25. f 1 = ( µ 1 -1) ? ? ? ? ? ? - 2 1 R 1 R 1 , here R 1 = 8 , R 2 = R ? R 1 f 1 1 1 - µ - = ? ? ? ? ? ? ? - - µ = 2 1 2 2 R 1 R 1 ) 1 ( f 1 . here R 1 = R and R 2 = 8 ? R 1 f 1 2 2 - µ = . Focal length of combination is R R 1 R 1 f 1 f 1 F 1 1 2 2 1 2 1 µ - µ + - µ + - µ - = + = ? F = 1 2 R µ - µ 26. (d) Assertion is false but reason is true. According to the dual character of light, it can act as a particle or as a wave but not both simultaneously. Some phenomenon, such as interference, diffraction can be explained only on the basis of its wave nature. Some other phenomenon such as photoelectric effect, black body radiation can be explained by both the wave theory as well as the corpuscular theory of light. The assertion is false but the reason is true as a special character of light is needed to explain some particular phenomenon. 27. (c) Assertion is true but reason is false. In an anisotropic medium the properties are not same in all direction. For an inhomogeneous medium the electric and magnetic properties differ at various positions in the medium. Thus the speed with which the secondary disturbance travels will vary and the wavefront will have a complicated shape. The reason is false a spherical wavefront cannot become a plane wavefront. Light emerging from a convex lens when a point source is placed at its focus is a parallel beam of light. This is equivalent to a point source at infinity produces a plane wavefront. The assertion is true. 28. (a) Both assertion and reason are true and reason is the correct explanation of the assertion. Let x be the path difference of the two waves from the slits reaching a point P at a distance y from the central fringe on the screen. Then x = D yd where d equals the distance between slits and D the perpendicular distance between slits & screen. In the case, the point of observation is directly opposite one of the slits, therefore y = . 2 d It is also given that the point P lies at the centre of the dark fringe (a minimum). Therefore x = (2n + 1) 2 ? . Combining x = . d 2 ) 1 n 2 ( D 2 d D yd 2 2 ? ? ? ? + = = 29. (d) Assertion is false but reason is true. The velocity of light in a medium depends upon wavelength. A narrow pulse of light is made of a Page 5 [1] (Wave & Ray Optics) 1. In Youngâ€™s double slit experiment if the slit widths are in the ratio 1 : 9, the ratio of the intensity at minima to that at maxima will be (a) 1 (b) 1/9 (c) 1/4 (d) 1/3 2. Which of the following statements are true for light waves but not for sound waves ? (i) the speed of wave is greater in vacuum than in a medium (ii) waves of different frequencies travels with different speeds in a medium (iii) Waves travel with different speeds in different media. Choose your answer according to the code given below : (a) (i) and (ii) (b) (i) and (iii) (c) (ii) and (iii) (d) (i), (ii) and (iii) 3. For sustained interference we need two sources which emit radiation : (a) with same intensity (b) with same amplitude (c) having constant phase difference (d) in a narrow beam. 4. The intensity of the light emerging from the two slits in Youngâ€™s experiment is in the ratio 1 to 4. The intensity of the minimum to the consecutive maximum will be in the ratio of : (a) 1 : 2 (b) 1 : 4 (c) 1: 9 (d) none of these 5. A thin film is viewed in white light. The colour of the film seen at a particular point depends upon: (a) width of the source (b) distance of the source (c) location of the observer (d) none of these 6. In Youngâ€™s double slit experiment the 7 th maximum with wavelength ? 1 is at a distance d 1 and that with wavelength ? 2 is at distance d 2 . Then d 1 /d 2 = (a) ? 1 / ? 2 (b) ? 2 / ? 1 (c) ? 2 1 / ? 2 2 (d) ? 2 2 / ? 2 1 7. A light of 6000 Å is used to produce interference pattern. The observed fringe width is 0.12 mm. The angle between two interfering wave trains is (a) 2 x 10 â€“3 radian (b)3 x 10 â€“3 radian (c) 4x 10 â€“3 radian (d) 5x 10 â€“3 radian. 8. In a biprism experiment by using light of wavelength 5000 Å, 5 mm wide fringes are obtained on a screen 1.0 m away from the coherent sources. The separation between the two coherent sources is (a) 1.0mm (b) 0.1mm (c) 0.05mm (d) 0.01mm 9. When the light is incident at the plarising angle, which of the following is completely polarised ? ? (a) Refracted light (b) Reflected light (c) both reflected as well as refracted (d) neither reflected nor refracted light 10. In Youngâ€™s double slit experiment, if the widths of the slit are in the ratio 4 : 9, ratio of intensity of maxima to intensity of minima will be (a) 25:1 (b) 9:4 (c) 3:2 (d) 81:16. 11. Doppler shift for the light of wavelength 6000Å emitted from the sun is 0.04Å. If radius of the sun is 7 x 10 8 m then time period of rotation of the sun will be (a) 30days (b) 365 days (c) 24 hours (d) 25 days. 12. In youngâ€™s double slit experiment a maximum is obtained when the path difference between the interfering waves is (Given that n = 1, 2, 3, 4â€¦.) (a) n 2 ? (b) n ? (c) (2n + 1) 2 ? (d) other than that given above 13. A piano-convex lens when silvered on the plane side behaves like a concave mirror of focal length 30 cm. When silvered on convex side, it behaves like a concave mirror of focal length 10 cm. The refractive index of material is (a) 3.0 (b) 2.0 (c) 2.5 (d) 1.5 14. Fig. shows the path of ray through an equiangular glass prism. It is incident on face AC at the critical angle for glass air interface. The angle of deviation of ray is 108°. Find the refractive index of glass prism. (a) 1.01 (b) 2.02 (c) 1.45 (d) 1.72 [2] 15. A thin prism of angle 5° is placed at a distance of 10 cm from the object. What is distance of image from the object? (a) 0.25 cm (b) 0.43 cm (c) 0.52 cm (d) 0.61 cm 16. The refractive index of the material of equilateral prism is 3 . The angle of minimum deviation for the prism is (a) 30° (b) 41° (c) 49° (d) 60°. 17. A light bulb is placed between two plane mirrors inclined at an angle of 60 °. The number of images formed are : (a) 6 (b) 2 (c) 5 (d) 4 18. What causes changes in the colours of the thin soap or oil films for the given beam of light ? (a) angle of incidence (b) angle of reflection (c) thickness of the film (d) none of these 19. Instead of using two slits as in Youngâ€™s experiment, if we use two separate but identical sodium lamps, which of the following will occur ? (a) General illumination (b) Widely separate interference (c) Very bright maximum (d) Very dark minimum 20. In Fresnelâ€™s biprism experiment, bands of width 0.185 mm are observed at a distance one meter from the slit. The image of the coherent sources is then produced at the same distance from the slit by placing a convex lens at 30 cm from the slit. The images are found to be separated by a distance of 0.70 cm. The wavelength of the light used is (a) 1295Å (b) 5550Å (c) 6000Å (d) 6500 Å 21. If two mirrors are kept at 60 ° to each other, then the number of images formed by them is (a) 5 (b) 6 (c) 7 (d) 8. 22. A light source approaches the observer with velocity 0.5c. Doppler shift for light of wavelength 5500 Å is (a) 616 Å (b) 1833 Å (c) 5500 Å (d) 6160 Å 23. On introducing a thin mica sheet of thickness 2 x 10 â€“6 m and refractive index 1.5 in the path of one of the waves, central bright maxima shifts by n fringes. Wavelength of the wave used is 5000 Å, then n is (a) 1 (b) 2 (c) 5 (d) 10. 24. The focal length of a lens in a camera is marked Æ’: 2.8 is 8 cm. What is diameter of lens? (a) 1.4 cm (b) 2.8 cm (c) 3.2 cm (d) 4.0 cm 25. A plano-convex lens fits exactly into a plano- concave lens. Their plane surfaces are parallel to each other. If the lenses are made of different materials, what is focal length of combination ? Given Æ’ 1 = focal length of piano-concave lens Æ’ 2 = focal length of piano-convex lens µ 1 = ref. index of material of piano-concave lens µ 2 = ref. index of material of piano convex lens. (a) R 1 2 µ - µ (b) 1 2 R µ - µ (c) R 2 1 µ µ (d) R 1 2 µ µ In every question a statement of ASSERTION is followed by a statement of REASON. Mark the correct answer out of the following choices: (a) If both ASSERTION and REASON are true and reason is the correct explanation of the assertion. (b) If both ASSERTION and REASON are true but reason is not the correct explanation of the assertion. (c) If ASSERTION is true but REASON is false. (d) If ASSERTION is false but REASON is true. 26. Assertion: According to dual theory, light has a particle and wave nature at the same time. Reason: Any, particle or wave nature of light may be needed to explain a particular phenomenon. 27. Assertion: Light emerging from a convex lens when a point source is placed at its focus produces a plane wavefront. [3] Reason: A spherical wavefront on entering an inhomogenous anisotropic medium becomes a plane wavefront. 28. Assertion: In Youngâ€™s double slit experiment if the point on the screen directly opposite to a slit is dark then the wavelength of the source is proportional to square of the distance between the slits. Reason: A minima is obtained when the path difference is (2n + 1) 2 ? and the phase difference is (2n + 1) p. 29. Assertion: A narrow pulse of light, through a medium retains its shape as it travels through the medium. Reason: A narrow pulse of light is made of harmonic waves with a large range of wavelengths. 30. Assertion: One of the two polaroids crossed to each other is rotated through 30 °. Only 1/8th of the incident unpolarised light passes through the combination. Reason: The amount of light going through the Polaroid is determined by Malusâ€™ law. ANSWER KEY 1 C 6 A 11 D 16 D 21 A 26 D 2 A 7 D 12 B 17 C 22 B 27 C 3 C 8 B 13 D 18 C 23 B 28 A 4 C 9 B 14 C 19 A 24 B 29 D 5 C 10 A 15 B 20 B 25 B 30 A SOLUTIONS 1. Amplitude of the superimposing waves are A 1 /A 2 = (1/9) 1/2 = 1/3 4 1 ) A A ( ) A A ( I I 2 2 1 2 2 1 ima max ima min = + - = 2. Speed of sound in vacuum is zero. Also there is no dispersion of sound wave. So both (i) and (ii) are not valid for sound waves. 3. (c) 4. Amplitude are in the ratio 1 : 2. Hence amplitude at minimum will be 1 and that at maximum will be 3. 5. (c) 6. 7 ß = 7 D ? 1 /d = d 1 and 7 ß 2 = 7D ?/d = d 2 Hence ? 1 / ? 2 = d 1 /d 2 7. Here ß = d D ? Angle ? between two waves train is ? = ß ? = D d or ? = 3 10 10 12 . 0 10 6000 - - × × \ 8. use ß = d D ? 9. (b) 10. 4 9 I I W W 2 1 2 1 = = ? 4 9 a a 2 2 2 1 = 2 3 a a 2 1 = a max = a 1 + a 2 a min = a 1 - a 2 ? min max I I = 1 25 ) a a ( ) a a ( 2 1 2 1 = - + 11. Dopplerâ€™s shift is given by ? ? = ? ? ? ? ? ? ? ? = ? c . R c v ? = T 2 p ? R. ? ? ? ? ? ? p T 2 . ? = ? d c T = days 25 c / . dr 2 . R = ? p 12. (b) 13. Focal length of plano -convex lens f 1 = 1 R - µ â€¦(1) (i) Focal length equivalent concave mirror, when one side of lens is silvered m m l f 1 R ) 1 ( 2 f 1 f 2 F 1 + - µ = + = â€¦â€¦..(2) (ii) When plane side is silvered, then f m = 8 , so eqn. (2) gives 8 + - µ = 1 R ) 1 ( 2 F 1 1 R ) 1 ( 2 30 1 - µ = (iii) When convex side of its silvered f m = 2 R , so eqn. (2) gives R 2 R 2 R ) 1 ( 2 F 1 2 µ = + - µ = R 2 10 1 µ = â€¦(4). Dividing (3) by (4) µ - µ = 1 30 10 ? µ = 3 ( µ - 1) or µ = 1.5 14. Let i be angle of incidence at Q. Then angle of refraction at Q is 90 ° - (180 ° - A - 90 ° + C) = A - C. Angle of incidence at S is also (A - C), so angle [4] of emergence at S is also i. Total deviation is algebraic sum of deviation at Q. R and S. 108 ° = i - (A - C) + 180 ° - 2C + i - (A -C) 2i - 2A + 180 ° = 2i - 120 ° + 180 ° or i = 24 ° µ = ) C 60 ( sin 24 sin r sin i sin - ° = After solving, µ = 1.45 15. D = ( µ - 1) A Distance of image from the object = OI = OE × D = µ × ( µ - 1) A ? OI = 10 (1.5 - 1) × cm 43 . 0 180 5 = ° × p 16. µ = 2 A sin 2 A sin r sin i sin d + = ° d + = 30 sin 2 A sin 3 , because A = 60 ° or sin ° = = d + 60 sin 2 3 2 A or A + d = 2 × 60 = 120 °. This gives d = 60 ° 17. Number of images N = 1 360 - ? . Where ? is in degrees. Here ? = 60 ° . Hence N = 5. 18. (c) 19. The superimposing waves will not be in constant phase. This leads to general illumination. 20. Here ß = 0.185 mm = 0.0185 cms D = 1.0 m = 100 cm u = = 30 cm ? v = 100 - 30 = 70 cm; Size of image, I = 0.70 cm Size of object, d = ? ? = ?. We know = v u image of size object of Size = 70 30 I d = d = cm 30 . 0 7 . 0 70 30 I 70 30 = × = × Now ? = 100 3 . 0 0185 . 0 D d × = ß = 555 × 10 - 7 cm = 5550 ? 21. (a) n = 60 360 -1 =5. 22. vâ€™ = ' c v c ? ? = + ? ?â€™ = 3667 c 5 . 0 c c 5500 v c c = + × = + ? Å ? ? ? = 95500 - 3667) = 1833 Å 23. shift is given by n ? = ( µ - 1) t. ? n = 2 t ) 1 ( = ? - µ 24. The meaning of mark f : 2.8 is that f is 2.8 times the aperture (diameter) of lens ? 8 = 2.8 × diameter or diameter = 8 . 2 cm 8 = 2.8 cm 25. f 1 = ( µ 1 -1) ? ? ? ? ? ? - 2 1 R 1 R 1 , here R 1 = 8 , R 2 = R ? R 1 f 1 1 1 - µ - = ? ? ? ? ? ? ? - - µ = 2 1 2 2 R 1 R 1 ) 1 ( f 1 . here R 1 = R and R 2 = 8 ? R 1 f 1 2 2 - µ = . Focal length of combination is R R 1 R 1 f 1 f 1 F 1 1 2 2 1 2 1 µ - µ + - µ + - µ - = + = ? F = 1 2 R µ - µ 26. (d) Assertion is false but reason is true. According to the dual character of light, it can act as a particle or as a wave but not both simultaneously. Some phenomenon, such as interference, diffraction can be explained only on the basis of its wave nature. Some other phenomenon such as photoelectric effect, black body radiation can be explained by both the wave theory as well as the corpuscular theory of light. The assertion is false but the reason is true as a special character of light is needed to explain some particular phenomenon. 27. (c) Assertion is true but reason is false. In an anisotropic medium the properties are not same in all direction. For an inhomogeneous medium the electric and magnetic properties differ at various positions in the medium. Thus the speed with which the secondary disturbance travels will vary and the wavefront will have a complicated shape. The reason is false a spherical wavefront cannot become a plane wavefront. Light emerging from a convex lens when a point source is placed at its focus is a parallel beam of light. This is equivalent to a point source at infinity produces a plane wavefront. The assertion is true. 28. (a) Both assertion and reason are true and reason is the correct explanation of the assertion. Let x be the path difference of the two waves from the slits reaching a point P at a distance y from the central fringe on the screen. Then x = D yd where d equals the distance between slits and D the perpendicular distance between slits & screen. In the case, the point of observation is directly opposite one of the slits, therefore y = . 2 d It is also given that the point P lies at the centre of the dark fringe (a minimum). Therefore x = (2n + 1) 2 ? . Combining x = . d 2 ) 1 n 2 ( D 2 d D yd 2 2 ? ? ? ? + = = 29. (d) Assertion is false but reason is true. The velocity of light in a medium depends upon wavelength. A narrow pulse of light is made of a [5] harmonic waves with a large range of wavelengths. The reason is the true. Each harmonic wave travels with a different speed in the medium. Thus the shape of the pulse is altered. The assertion is not true. 30. (a) Both assertion and reason are true and reason is correct explanation of the assertion. Malus law states that when plane polarized light passes through a polarizer, then the intensity I is according to I ? cos 2 ? or I = I 0 cos 2 ?. Where I 0 is the intensity of plane polarized light and ? is the angle between the plane of transmission and the polarizer. When one of the polaroids is rotated through 30 °, the angle ? between the plane of vibration and the axis is = 90 ° - 30 ° = 60 °. Therefore, I = I 0 cos 2 60 ° = 4 I 0 . If Iâ€™ is the intensity of the unpolarised light, then the intensity of plane polarized light produced by the first Polaroid is . 2 ' I Therefore, I = 8 ' I 4 I 2 ' I 4 I 0 = = . The reason is correct and leads to the correct value given in the assertion.Read More

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