Questions OBJECTIVE - II and Answer (Dispersion and Spectra) HC Verma Part 1

 Q#1

A narrow beam of white light goes through a slab having parallel faces.
(a) The light never splits in different colors.
(b) The emergent beam is white.
(c) The light inside the slab is split into different colors.
(d) The light inside the slab is white.
Answer: (b), (c).

When the light enters the slab, the different colors of light go through different deviation after the refraction. Hence inside the slab, the light splits in different colors. Options (a) and (d) are not true but (c) is true.

When these lights exit through the parallel side of the slab, the second refraction makes the split light reunite because they suffer equal and opposite deviation. Thus the emergent beam is white. Option (b) is true.

Q#2
By properly combining two prisms made of different materials, it is possible to
(a) have dispersion without average deviation.
(b) have deviation without dispersion.
(c) have both dispersion and average deviation.
(d) have neither dispersion nor average deviation.

Answer: (a), (b), (c).
For the net average deviation = 0,

(µ - 1)A = (µ' - 1)A'  ------------------- (i)

And the net angular dispersion produced is

𝛿ᵥ - 𝛿ᵣ = (µ - 1)A(⍵ - ⍵')

By choosing ⍵ and ⍵' different and the refracting angles to satisfy (i) we can get dispersion without average deviation. Optio (a) is true.
  
For the combination to produce a net dispersion = 0, the net average deviation produced is

𝛿 = (µᵧ - 1)A{1 - ⍵/⍵'}

So the option (b) is also true.
It is a general case to have both dispersion and net average deviation. So the option (c) is also true.
Since (a), (b), and (c) are true the option (d) will not be true.

Q#3
In producing a pure spectrum, the incident light is passed through a narrow slit placed in the focal plane of an achromatic lens because a narrow slit
(a) produces less diffraction
(b) increases intensity
(c) allows only one color at a time
(d) allows a more parallel beam when it passes through the lens.

Answer: (d)
If the slit is not narrow, the different points of the slit act as different sources and when they pass through the lens the emergent rays are not so parallel. Thus an impure spectrum is produced. Hence the option (d).

Q#4
Which of the following quantities related to a lens depend on the wavelength or wavelengths of the incident light?
(a) Power.
(b) Focal length.
(c) Chromatic aberration.
(d) Radii of curvature.

Answer: (a), (b), (c).
Since the refractive index of a medium depends on the wavelength of the incident light, the focal length of the lens depends on the wavelength {Option (a)}. Hence the power of the lens which is reciprocal of the focal length also depends on the wavelength {Option (b). Since a lens has a different focal length for different wavelengths, it can not form the image at the same point. It is called Chromatic aberration. So it also depends on the wavelengths of the incident light {Option(c)}.
Radii of curvature of a lens are its geometric property and fixed. It does not depend on the wavelength of the incident light. Option (d) is not correct.

Q#5
Which of the following quantities increase when the wavelength is increased? Consider only the magnitudes.
(a) The power of a converging lens.
(b) The focal length of a converging length.
(c) The power of a diverging lens.
(d) The focal length of a diverging lens.

Answer: (b), (d).
More the wavelength less is the deviation of the refracted rays and hence longer the focal length (f). Hence the option (b) and (d) are true. The power if a lens P = 1/f, hence with an increase in the wavelength, f increases, and P decreases. So the options (a) and (c) are not true.