HC Verma solutions for Concepts of Physics Volume 1 and 2 [English] chapter 20 - Dispersion and Spectra [Latest edition]

The equation \[\omega = \frac{\mu_u - \mu_r}{\mu - 1}\] was derived for a prism having small refracting angle. Is it also valid for a prism of large refracting angle? Is it also valid for a glass slab or a glass sphere?

Can the dispersive power \[\omega = \frac{\mu_u - \mu_r}{\mu - 1}\] be negative? What is the sign of ω if a hollow prism is immersed into water?

If three identical prisms are combined, is it possible to pass a beam that emerges undeviated? Undispersed?

"Monochromatic light should be used to produce pure spectrum". Comment on this statement.

Does focal length of a lens depend on the colour of the light used? Does focal length of a mirror depend on the colour?

Suggest a method to produce a rainbow in your house.

The angular dispersion produced by a prism ___________ .

If a glass prism is dipped in water, its dispersive power ___________ .

A prism can produce a minimum deviation δ in a light beam. If three such prisms are combined, the minimum deviation that can be produced in this beam is _______________.

Consider the following two statements :-

(A) Line spectra contain information about atoms.

(B) Band spectra contain information about molecules.

The focal length of a converging lens are f_v and f_r for violet and red light respectively.

A narrow beam of white light goes through a slab having parallel faces.

(a) The light never splits in different colours

(b) The emergent beam is white

(c) The light inside the slab is split into different colours

(d) The light inside the slab is white

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

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 ___________ .

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

Which of the following quantities increase when wavelength is increased? Consider only the magnitudes.

(a) The power of a converging lens

(b) The focal length of a converging lens

(c) The power of a diverging lens

(d) The focal length of a diverging lens

A flint glass prism and a crown glass prism are to be combined in such a way that the deviation of the mean ray is zero. The refractive index of flint and crown glasses for the mean ray are 1.620 and 1.518 respectively. If the refracting angle of the flint prism is 6.0°, what would be the refracting angle of the crown prism?

A certain material has refractive indices 1.56, 1.60 and 1.68  rfor red, yellow and violet lightespectively. (a) Calculate the dispersive power. (b) Find the angular dispersion produced by a thin prism of angle 6° made of this material.

The focal lengths of a convex lens for red, yellow and violet rays are 100 cm, 98 cm and 96 cm respectively. Find the dispersive power of the material of the lens.

The refractive index of a material changes by 0.014 as the colour of the light changes from red to violet. A rectangular slab of height 2.00 cm made of this material is placed on a newspaper. When viewed normally in yellow light, the letters appear 1.32 cm below the top surface of the slab. Calculate the dispersive power of the material.

A thin prism is made of a material having refractive indices 1.61 and 1.65 for red and violet light. The dispersive power of the material is 0.07. It is found that a beam of yellow light passing through the prism suffers a minimum deviation of 4.0° in favourable conditions. Calculate the angle of the prism.

The minimum deviations suffered by, yellow and violet beams passing through an equilateral transparent prism are 38.4°, 38.7° and 39.2° respectively. Calculate the dispersive power of the medium.

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?

Three thin prisms are combined as shown in figure. The refractive indices of the crown glass for red, yellow and violet rays are μ_r, μ_y and μ_v respectively and those for the flint glass are μ'_r, μ'_y and μ'_v respectively. Find the ratio A'/A for which (a) there is no net angular dispersion, and (b) there is no net deviation in the yellow ray.

A thin prism of crown glass (μ_r = 1.515, μ_v = 1.525) and a thin prism of flint glass (μ_r = 1.612, μ_v = 1.632) are placed in contact with each other. Their refracting angles are 5.0° each and are similarly directed. Calculate the angular dispersion produced by the combination.

A thin prism of angle 6.0°, ω = 0.07 and μ_y = 1.50 is combined with another thin prism having ω = 0.08 and μ_y = 1.60. The combination produces no deviation in the mean ray. (a) Find the angle of the second prism. (b) Find the net angular dispersion produced by the combination when a beam of white light passes through it. (c) If the prisms are similarly directed, what will be the deviation in the mean ray? (d) Find the angular dispersion in the situation described in (c).

The refractive index of a material M1 changes by 0.014 and that of another material M2 changes by 0.024 as the colour of the light is changed from red to violet. Two thin prisms, one made of M1(A = 5.3°) and the other made of M2(A = 3.7°) are combined with their refracting angles oppositely directed. (a) Find the angular dispersion produced by the combination. (b) The prisms are now combined with their refracting angles similarly directed. Find the angular dispersion produced by the combination.