Question

If the ratio of dispersive powers of the materials of two prisms be $2:3$ and ratio of angular dispersions produced by them is $1:2$, then the ratio of mean deviation produced by them is:

• A. $4:3$
• B. $3:4$
• C. $1:3$
• D. $3:1$

Answer 1

The correct option is B $3:4$

We have,
$w=\frac{\delta }{D}$

where $w$ is dispersive power, $\delta$ is angular dispersion and $D$ is the mean deviation.
If we consider two materials then we have
$w=\frac{\delta }{D}$ and $w^1=\frac{{\delta }^{\prime }}{D^{\prime }}$

$⟹\frac{w}{w^1}=\frac{\delta }{D}\times \frac{D^1}{{\delta }^1}$

Given $\frac{w}{w^1}=\frac{2}{3}$ and $\frac{\delta }{{\delta }^1}=\frac{1}{2}$

$⟹\frac{D}{D^1}=\frac{3}{4}$

i.e., $D:D^1=3:4$