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1.

The focal length ofa converging lens are `f_v and f_r` for violet and red light respectively.A. `f_vgtf_r`B. `f_v=f_r`C. `f_vltf_r`D. Any of the three is possible depending on the value of the average refractive index `mu`.

Answer» Correct Answer - C
Discussion
2.

The focal lengths of a thin lens for red and violet light are 90.0 cm and 86.4cm respectively. Find the dispersive power of the material of the lens. Make appropriate assumptons.

Answer» We have
`(1)/(f) = (mu-1) ((1)/(R_1) - (1)/(R_2))`
`or `mu - 1 = (1)/(f). (1)/((1)/(R_1) - (1)/(R_2)) = (K)/(f).`
Thus, `mu_(upsilon) -1 = (K)/(f_(upsilon))`
and `mu_r - 1=(K)/(f_r)`
so that `mu_(upsilon) - mu_r = K((1)/(f_(upsilon)) - (1)/(f_r))`
`=K[(1)/(85.4 cm) - (1)/(90cm)] =Kxx4.6 xx 10^(-4) cm^(-1)`
Also, we can assume that
`mu_y -1 = (mu_(upsilon) + mu_r)/(2) -1 = (mu_(upsilon) - 1)/(2) + (mu_(upsilon)-1)/(2)`
`(K)/(2) ((1)/(f_(upsilon) + (1)/(f_r))`
`=(K)/(2) [(1)/(86.4 cm) + (1)/(90cm)] = Kxx1.1xx10^(-2)cm^O(-1)`
Thus, the dispervise power of the meterial of the lens
`omega= (mu_(upsilon) - mu_r)/(mu_y - 1) = (4.6xx 10^(-4))/(1.1xx10^(-2)) = 0.042.`
Discussion
3.

In producing a pure specturm, the incident light is passed through a narrow slit placed i the focal plane of an chromatic lens because a narrow slitA. a produces less diffractionB. increases intensityC. allows onlyone colour at a timeD. allows miore paralle beam whenit pases thorugh the lens

Answer» Correct Answer - D
Discussion
4.

Which of the following quantities increae when wavelength in increased? Consider only the magnitudesA. the power of a converging lensB. the focasl length of a converging lensC. the power of a diverging lensD. the focal length of a diverging lens.

Answer» Correct Answer - B::D
Discussion
5.

By properly combining two prisms made of different materials, it is possible toA. have disersion whitout average deviationB. have deviation without dispersionC. have both dispersion and average deviationD. have neither dispersion nor average deviation.

Answer» Correct Answer - A::B::C
Discussion
6.

Two prisms of identical geometrical shape are combined with their refracting angles oppositely directed. The materials of the prisms have refractive indices 1.52 and 1.62 for violet light. A violet ray is deviated by `1.0^@` when passes symmetrically through this combination. What is the angle of the prisms ?

Answer» Correct Answer - A
Two prisms of identical geometrical shape are combined
`Ler A=angle of the prisms
`mu_y=1.52 and mu_y=1.62`
`mu_y=1.0^@`
`delta_y=(mu_y-1)A-(mu_y-1)A` [since A=a]
`delta_y=(mu_y-mu_y)A`
`A=delta_y/(mu_y=mu_y)=1/((1.62)-(1.52))`
`=1/0.1=10^@`
Discussion
7.

If a glass prism in dipped in water its dispersive powerA. increasesB. decreasesC. does not changeD. may increase or decrease depedig on whether the angle of the prism is less than or greater than `60^@`

Answer» Correct Answer - B
Discussion
8.

The refractive index of a material `M_1` changes by `0.014` and that of another material `M_2` changes by `0.024` as the colour of the light is changed from red to violet. Two thin prisms one made of `M_1 (A = 5.3^@)` and other made of `M_2(A = 3.7^@)` are combined with their refracting angles oppositely directed. (a) Find the angular dispesion produced by the combination. (b) the prisms are now combined with their refracting angles similarly directed. Find the angular dispersion produced by the combination.

Answer» Correct Answer - A::B::C::D
Discussion
9.

Which of the following quantities related to a lens depend on the wavelength or wavelengths of the incident light? (Choose the incorrect option)A. powerB. focal lengthC. chromatic aberrationD. radii of curvature

Answer» Correct Answer - A::B::C
Discussion