J J Science Academy - Test Paper

1. A transparent cube of 15 cm edge contains a small air bubble. Its apparent depth, when viewed through one face is 6 cm and when viewed through the opposite face is 4 cm . Then the refractive index of the material of the cube is

(1) $2.0$ (2) $2.5$ (3) $1.6$ (4) $1.5$

2. A fish at a depth of 12 cm in water is viewed by an observer on the bank of a lake. To what height the image of the fish is raised.

(1) $9 cm$ (2) $12 cm$ (3) $3.8 cm$ (4) $3 cm$

3. Keeping the incident ray fixed, if plane mirror is rotated through an angle '$\theta$' about an axis lying in its plane, then the reflected ray turns through an angle of

(1) $\theta$ (2) $2 \theta$ (3) $\frac{\theta}{2}$ (4) $4 \theta$

4. Critical angle of light passing from glass to air is minimum for

(1) $red.$ (2) $green.$ (3) $yellow.$ (4) $violet.$

5. White light is incident on the interface of glass and air as shown in the figure. If green light is just totally internally reflected, then the emerging ray in air contains

(1) $yellow, orange, red.$ (2) $violet, indigo, blue.$ (3) $all colours.$ (4) $all colours except green.$

6. A ray of light travelling inside a rectangular glass block of refractive index $\sqrt{2}$ is incident on the glass- air surface at an angle of incidence of $45^{\circ}$. The refractive index of air is one. Under these conditions the ray

(1) $will emerge into the air without any deviation.$ (2) $will be reflected back into the glass.$ (3) $will be absorbed.$ (4) $will emerge into the air with an angle of refraction equal to 90^{\circ}.$

7. A ray of light travels from glass (refractive index $= \frac{3}{2}$) to water (refractive index $= \frac{4}{3}$). The value of the incident angle, at which the ray of light does not emerge from water, is

(1) $\sin ^{-1}(\frac{1}{2})$ (2) $\sin ^{-1}(\frac{\sqrt{8}}{9})$ (3) $\sin ^{-1}(\frac{8}{9})$ (4) $\sin ^{-1}(\frac{5}{7})$

8. Two transparent media A and B are separated by a plane boundary. The speed of light in medium A is $2.0 \times 10^{8} m / s$ and in medium B is $2.5 \times 10^{8} m / s$. The critical angle for which a ray of light going from A to B is totally internally reflected is

(1) $\sin ^{-1}(\frac{5}{4})$ (2) $\sin ^{-1}(\frac{2}{5})$ (3) $\sin ^{-1}(\frac{4}{5})$ (4) $\sin ^{-1}(\frac{1}{2})$

9. A light ray is incident perpendicular to one face of a $90^{\circ}$ prism and is totally internally reflected at the glass-air interface. If the angle of reflection is $45^{\circ}$, we conclude that the refractive index $n=$

(1) $n<\frac{1}{\sqrt{2}}$ (2) $n>\sqrt{2}$ (3) $n>\frac{1}{\sqrt{2}}$ (4) $n<\sqrt{2}$

10. The refractive index of water is (4/3) and that of a given slab of glass is $(3 / 2)$. If the speed of light in glass is $2 \times 10^{8} m / s$, then the speed of the light in water will be

(1) $1 \times 10^{8} m / s$ (2) $\frac{9}{4} \times 10^{8} m / s$ (3) $\frac{8}{3} \times 10^{8} m / s$ (4) $4 \times 10^{8} m / s$

11. A fish rising vertically up towards the surface of water with speed $3 m / s$ observes a bird diving vertically down towards it with speed $9 m / s$. The actual velocity of bird is [Given : $\mu=\frac{4}{3}$)]

(1) $4.5 ms^{-1}$ (2) $5.4 ms^{-1}$ (3) $3.0 ms^{-1}$ (4) $3.4 ms^{-1}$

12. Refractive index of glass is $3 / 2$ and refractive index of water is $4 / 3$. If the speed of light in water is $1.5 \times 10^{8} m / s$, the speed in glass will be

(1) $2.67 \times 10^{8} m / s$ (2) $2.25 \times 10^{8} m / s$ (3) $1.33 \times 10^{8} m / s$ (4) $1.50 \times 10^{8} m / s$

13. Material A has critical angle $i_{A}$, and material B has critical angle $i_{B}(i_{B}>i_{A})$. Then which of the following is true? (i) Light can be totally internally reflected, when it passes from B to A. (ii) Light can be totally internally reflected when it passes from A to B. (iii) Critical angle for total internal reflection is $i_{B}-i_{A}$. (iv) Critical angle between A and B is $\sin ^{-1}(\frac{\sin i_{A}}{\sin i_{B}})$.

(1) $(i) and (iii)$ (2) $(i) and (iv)$ (3) $(ii) and (iii)$ (4) $(ii) and (iv)$

14. A ray of light strikes a glass at an angle of $60^{\circ}$. If the reflected and refracted rays are perpendicular to each other, the refractive index of glass is

(1) $\frac{\sqrt{3}}{2}$ (2) $\frac{3}{2}$ (3) $\frac{1}{2}$ (4) $\sqrt{3}$

15. A monochromatic beam of light is travelling from medium ' A ' of refractive index ' $n_{1}$' to a medium ' B ' of refractive index ' $n_{2}$'. In the medium ' A ', there are ' x ' number of waves in certain distance. In the medium ' $B$', there are ' y ' number of waves in the same distance. The ratio of refractive index of medium ' A ' with respect to that of medium ' B ' is

(1) $\frac{y}{x-y}$ (2) $\sqrt{\frac{x}{y}}$ (3) $\frac{x}{y-x}$ (4) $\frac{x}{y}$

16. A beam of light is incident at $60^{\circ}$ to a plane surface. The reflected and refracted rays are perpendicular to each other. The refractive index of the surface is

(1) $\frac{1}{\sqrt{3}}$ (2) $\sqrt{3}$ (3) $\frac{1}{3}$ (4) $3$

17. On heating a liquid, the refractive index generally

(1) $decreases.$ (2) $increases or decreases depending on the rate of heating.$ (3) $does not change.$ (4) $increases.$

18. A ray of light enters 4 rectangular parallel slabs placed in series. The R.I. of the slabs is $n_{1}, n_{2}, n_{3}, n_{4}$. If the ray of light is found to be parallel in medium 2 and 4 , then

(1) $n_{1}+n_{2}=n_{3}+n_{4}$ (2) $n_{1}-n_{3}=n_{2}-n_{4}$ (3) $n_{1}=n_{3}$ (4) $n_{2}=n_{4}$

19. What is the time taken (in second) to cross a glass of thickness 2 mm and $\mu=2$ by light?

(1) $4 \times 10^{-11}$ (2) $1.34 \times 10^{-11}$ (3) $2 \times 10^{-11}$ (4) $3 \times 10^{-11}$

20. The speed of light in water is three-fourth of that in air. If wavelength of light in air is $6000 \AA$, then its wavelength in water and refractive index of water are respectively

(1) $4000 \AA, 1.12$ (2) $4500 \AA, 1.12$ (3) $4000 \AA, 1.33$ (4) $4500 \AA, 1.33$

21. A ray of light travels from glass (R.I. 1.5) to diamond (R.I. 2.5) and is incident at a small angle of incidence i. It will be deviated by an angle of

(1) $\frac{2}{5} i$ (2) $\frac{5}{3} i$ (3) $\frac{3}{2} i$ (4) $\frac{2}{3} i$

22. The wave number of a beam in air is X . The number of waves of the beam contained in d cm of a medium of R.I. n , is

(1) $\frac{X n}{d}$ (2) $d n X$ (3) $\frac{n d}{X}$ (4) $\frac{X}{n d}$

23. A glass slab of thickness 4 cm contains the same number of waves as X cm of water column when both are traversed by the same monochromatic light. If the refractive indices of glass and water (for that light) are $5 / 3$ and $4 / 3$ respectively, then the value of X will be

(1) $\frac{5}{16} cm$ (2) $\frac{20}{9} cm$ (3) $\frac{16}{5} cm$ (4) $5 cm$

24. A ray of light in incident on one surface of a glass prism as shown. If the emergent ray moves parallel to the other surface, then angle of incidence on other surface is

(1) $A$ (2) $90-A$ (3) $90+A$ (4) $\frac{A}{2}$

25. For a small angled prism, angle of prism A, the angle of minimum deviation $(\delta)$ varies with the refractive index $(\mu)$ of the prism as shown in the graph. Then,

(1) $point P corresponds to m=1.$ (2) $slope of the line PQ=A / 2.$ (3) $slope = 2 A.$ (4) $None of the above statements is true.$

26. The minimum deviation produced by a glass prism of angle $60^{\circ}$ is $30^{\circ}$. If the velocity of light in vacuum is $3 \times 10^{8} m / s$, then the velocity of light in glass is

(1) $2.9 \times 10^{8} m / s$ (2) $2.12 \times 10^{8} m / s$ (3) $2.72 \times 10^{8} m / s$ (4) $1.8 \times 10^{8} m / s$

27. A certain prism is such that it produces a minimum deviation of $38^{\circ}$. It produces a deviation of $44^{\circ}$ when the angle of incidence is either $42^{\circ}$ or $62^{\circ}$. The refractive index of material of prism is

(1) $1.50$ (2) $1.33$ (3) $1.414$ (4) $1.732$

28. The refractive index of the material of prism is $\mu$ and its refracting angle is A . A ray of light will not emerge out of a prism, whatever be the angle of deviation, if

(1) $\mu=\sin (\frac{A}{2})$ (2) $\mu=\cos (\frac{A}{2})$ (3) $\mu>\sec (\frac{A}{2})$ (4) $\mu>\operatorname{cosec}(\frac{A}{2})$

29. For a prism $(PQR(PQ=QR))$, the incident and emergent rays are parallel as shown in figure below. The minimum value of refractive index of the prism material is

(1) $\sqrt{3}$ (2) $1.5$ (3) $\sqrt{2}$ (4) $2$

30. For a glass prism (R.I. $\sqrt{3}$), if the angle of the prism is equal to the angle minimum deviation, then the angle of the prism is

(1) $55.6^{\circ}$ (2) $33.5^{\circ}$ (3) $45^{\circ}$ (4) $60^{\circ}$

31. The minimum deviation for a ray of light through a prism is $44^{\circ}$ and when this happens the angle of incidence is $50^{\circ}$. The refracting angle of the prism is

(1) $64^{\circ}$ (2) $60^{\circ}$ (3) $56^{\circ}$ (4) $50^{\circ}$

32. A ray of light, incident on one face of an equilateral prism, undergoes total internal reflection at another face. If the refractive index of the material of prism is $\sqrt{2}$, then angle of refraction ($r_{2}$) at another face will be

(1) $15^{\circ}$ (2) $30^{\circ}$ (3) $45^{\circ}$ (4) $\sin ^{-1}(\sqrt{2} \sin 15^{\circ})$

33. What is the angle of incidence for an equilateral prism of refractive index $\sqrt{3}$ so that the ray is parallel to the base inside the prism?

(1) $30^{\circ}$ (2) $45^{\circ}$ (3) $60^{\circ}$ (4) $either 30^{\circ} or 60^{\circ}$

34. A prism of refractive index 1.5 is placed in water of refractive index 1.33. The refracting angle of a prism is $60^{\circ}$. What is the angle of minimum deviation in water? (Given $\sin 34^{\circ}=0.56$)

(1) $4^{\circ}$ (2) $8^{\circ}$ (3) $12^{\circ}$ (4) $16^{\circ}$

35. A prism $(\mu=1.5)$ has the refracting angle of $30^{\circ}$. The deviation of a monochromatic ray incident normally on its one surface will be $(\sin 48^{\circ} 36^{\prime}=0.75)$

(1) $18^{\circ} 36^{\prime}$ (2) $20^{\circ} 30^{\prime}$ (3) $18^{\circ}$ (4) $22^{\circ} 1^{\prime}$

36. The net angular dispersion without deviation produced by combination of crown glass prism $(A, \delta, \omega)$ and flint glass prism $(A^{\prime}, \delta^{\prime}, \omega^{\prime})$ is given by

(1) $\delta(1-\frac{\omega}{\omega^{\prime}})$ (2) $\delta(1-\frac{\omega^{\prime}}{\omega})$ (3) $\frac{\delta}{2}(\omega^{\prime}-\omega)$ (4) $\delta(\omega-\omega^{\prime})$

37. Which of the following colours of white light deviated most when passes through a prism?

(1) $Red light$ (2) $Violet light$ (3) $Yellow light$ (4) $Both (a) and (b)$

38. If angle of deviation by a thin prism made of glass $({ }_{a} \mu_{g}=3 / 2)$ in air is $\delta$. Now this prism is immersed in water $({ }_{a} \mu_{w}=4 / 3)$, the new angle of deviation will be

(1) $\delta$ (2) $\delta / 2$ (3) $\delta / 3$ (4) $\delta / 4$

39. If the refractive indices of crown glass for red, yellow and violet colours are 1.5140, 1.5170 and 1.5318 respectively and for flint glass these are $(1.6434,1.6499)$ and 1.6852 respectively, then the dispersive power for crown and flint glass are respectively

(1) $0.034 and 0.064$ (2) $0.064 and 0.034$ (3) $1.3 and 0.064$ (4) $0.034 and 1.0$

40. The refractive indices of violet and red light are 1.54 and 1.52 respectively. If the angle of prism is $10^{\circ}$, the angular dispersion in degree is

(1) $0.02^{\circ}$ (2) $0.20^{\circ}$ (3) $3.06^{\circ}$ (4) $30.6^{\circ}$

41. Dispersive power depends upon

(1) $the shape of prism.$ (2) $material of prism.$ (3) $angle of prism.$ (4) $height of the prism.$

42. Refractive index of a particular material is 1.67 for blue light and 1.63 for red light. The dispersive power of material is

(1) $0.024$ (2) $0.031$ (3) $0.0615$ (4) $1.6015$

43. The dispersive power of crown and flint glasses are 0.03 and 0.05 . If the difference in the refractive indices for blue and red colour is 0.015 and 0.022 for crown and flint glass, then the total deviation produced by two without dispersion is [Angles of the two prisms are $10^{\circ}$ and $6.8^{\circ}$]

(1) $5^{\circ}$ (2) $2^{\circ}$ (3) $5.5^{\circ}$ (4) $6^{\circ}$

44. A thin prism $P_{1}$ with angle $4^{\circ}$ and made from glass of refractive index 1.54 is combined with another prism $P_{2}$ made from glass of refractive index 1.72 to produce dispersion without deviation. The angle of prism $P_{2}$ is

(1) $5.33^{\circ}$ (2) $4^{\circ}$ (3) $3^{\circ}$ (4) $2.6^{\circ}$

45. Rainbow is an example of which phenomenon?

(1) $Refraction and Scattering$ (2) $Refraction and Total internal reflection$ (3) $Dispersion and Reflection$ (4) $Dispersion and Total internal reflection$