Q#1
The angular dispersion produced by a prism(a) increases if the average refractive index increases
(b) increases if the average refractive index decreases
(c) remains constant whether the average refractive index increases or decreases
(d) has no relation with the average refractive index.
Answer: (a)
The angular dispersion ẟᵥ - ẟᵣ depends on the average refractive index µ. With the increase in µ, the angular dispersion ẟᵥ - ẟᵣ also increases. For example, fluorite with a small µ has small angular dispersion while flint glass with high µ has larger angular dispersion.
Q#2
If a glass prism is dipped in water, its dispersive power
(a) increases
(b) decreases
(c) does not change
(d) may increase or decrease depending on whether the angle of the prism is less than or greater than 60°.
Answer: (b)
The average refractive index of prism decreases in water hence the angular dispersion will also decrease. So, the dispersive power will also decrease.
Q#3
A prism can produce a minimum deviation ẟ in a light beam. If three such prisms are combined, the minimum deviation that can be produced in this beam is
(a) 0
(b) ẟ
(c) 2ẟ
(d) 3ẟ.
Answer: (b)
If three identical prisms are combined side by side, they will have two types of combination:-
- All of them have vertices touching together or
- One of them is in a reverse manner, i.e. two vertices and one base touching together.
In the first case, the refracting angle of the combined prism will be three times the single one. So the minimum deviation, in this case, will be 3ẟ.
In the second case, one up and other down prisms will make a slab and no deviation. only minimum deviation will be through the third prism equal to ẟ. Hence the answer (b).Q#4
Consider the following two statements:
(A) Line spectra contain information about atoms.
(B) Band spectra contain information about molecules.
(a) both A and B are wrong
(b) A is correct but B is wrong
(c) B is correct but A is wrong
(d) both A and B are correct.
Answer: (d)
The light emitted by one kind of atoms generally have widely separated wavelength components. When this light is dispersed by a high-resolution grating, one obtains some lines on a dark background. This is called a line spectrum. So line spectra contain information about atoms.
The wavelengths emitted by a molecule are grouped and the wavelengths in a group are close to one another and appear as continuous. The spectrum looks like separate bands of varying colors. Such spectrum is called a band emission spectrum and it contains information about molecules.
Hence both statements (A) and (B) are true.
Q#5
The focal lengths of a converging lens are fᵥ and fᵣ for violet and red light respectively.
(a) fᵥ > fᵣ
(b) fᵥ = fᵣ
(c) fᵥ < fᵣ
(d) Any of the three is possible depending on the value of the average refractive index µ.
Answer: (c)
Since the deviation is more for shorter wavelengths, the deviation of violet light is more than the red light. The focal length of a converging lens is the distance of the focus (where the parallel light beam along the axis converges after refraction) from the optical center. Due to more deviation, the violet light beams will converge at a point nearer to the optical center than the red light beams. Hence, fᵥ < fᵣ. The option (c) is correct.
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