Question

The minimum deviations suffered by red, yellow, and violet beams passing through an equilateral transparent prism are ${38.4}^{\circ },{38.7}^{\circ }$ and ${39.2}^{\circ }$ respectively. Calculate the dispersive power of the medium.

• A. $0.0721$
• B. $0.0555$
• C. $0.0015$
• D. $0.0207$

Answer 1

The correct option is D $0.0207$

Given,

$({\delta }_r{)}_m={38.4}^{\circ };({\delta }_y{)}_m={38.7}^{\circ };({\delta }_v{)}_m={39.2}^{\circ }$

As we know, the minimum deviation suffered is,

$\therefore {\delta }_m=(\mu -1)A.....\left(1\right)$

Dispersive power is given by,

$\omega =\frac{{\mu }_v-{\mu }_r}{{\mu }_y-1}=\frac{({\mu }_v-1)-({\mu }_r-1)}{({\mu }_y-1)}.....\left(2\right)$

Using (1) we can rewrite (2) as follows,

$\omega =\frac{\frac{({\delta }_v{)}_m}{A}-\frac{({\delta }_r{)}_m}{A}}{\frac{({\delta }_y{)}_m}{A}}=\frac{({\delta }_v{)}_m-({\delta }_r{)}_m}{({\delta }_y{)}_m}$

$\Rightarrow \omega =\frac{39.2-38.4}{38.7}\approx 0.0207$

So, the dispersive power of the medium is $0.0207$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.

Why this question ? Concept : If the angle of minimum deviation for red, violet and yellow light are given, then the dispersive power can be calculated using the formula- $\Rightarrow \omega =\frac{({\delta }_v{)}_m-({\delta }_r{)}_m}{({\delta }_y{)}_m}$