Question

Dispersive power of the material of a prism is 0.0221. If the deviation produced by it for yellow colour is ${{38}^{\circ }}$, then the angular dispersion between red and violet colours is
 A. ${{0.65}^{\circ }}$
B. ${{0.84}^{\circ }}$
C. ${{0.48}^{\circ }}$
D. ${{1.26}^{\circ }}$

Answer 1

Hint:Angular dispersion is the measure of angular separation of the rays of light with different colour or wavelength that passes through a refractive surface like grating or prism, and it is equal to the rate of change of angle of deviation in accordance to wavelength variation.

Complete step by step answer:
Dispersive power of a prism is defined as the ratio of angular dispersion to the mean deviation produced by the prism.In the question, we are given the deviation produced for yellow colour.Hence mean deviation= ${{38}^{\circ }}$
Let the dispersive power be $\omega $, angular dispersion for red be ${{\delta }_{R}}$ and angular dispersion for violet be ${{\delta }_{V}}$and mean deviation be ${{\delta }_{Y}}$
\[\begin{align}
& \omega =\dfrac{{{\delta }_{V}}-{{\delta }_{R}}}{{{\delta }_{Y}}} \\
& \Rightarrow 0.0221=\dfrac{{{\delta }_{V}}-{{\delta }_{R}}}{{{38}^{\circ }}} \\
& \Rightarrow {{\delta }_{V}}-{{\delta }_{R}}={{0.84}^{\circ }} \\
\end{align}\]

Hence, the angular dispersion between red and violet colors is ${{0.84}^{\circ }}$ and option B is the correct answer among the given four options.

Note:Dispersive power of prism is also defined as the measure of the difference in refraction of the light of the highest wavelength and the lowest wavelength that enters the prism. Dispersive power of the prism can also be expressed in terms of the angle between the two extreme wavelengths. As the dispersive power increases, the angle between them increases, and vice versa. Also, yellow colour is always considered to be the dispersive power of the prism, as it is considered to be the mean ray.