Question

A thin prism of glass is placed in air and water respectively. If $n_g=\frac{3}{2}$ and $n_w=\frac{4}{3}$, then the ratio of deviation produced by the prism for a small angle of incidence when placed in air and water separately is:

• A. $9:8$
• B. $4:3$
• C. $3:4$
• D. $4:1$

Answer 1

The correct option is D $4:1$

The deviation produced by a thin prism when it is kept in air is,

${\delta }_a={(}_a{\mu }^g-1)A$

The deviation produced by the thin prism when it is kept in water is,

${\delta }_w={(}_w{\mu }^g-1)A$

$\Rightarrow \frac{{\delta }_a}{{\delta }_w}=\frac{{(}_a{\mu }^g-1)}{{(}_w{\mu }^g-1)}$

or, $\frac{{\delta }_a}{{\delta }_w}=\frac{(\frac{{\mu }_g}{{\mu }_a}-1)}{(\frac{{\mu }_g}{{\mu }_w}-1)}$

or, $\frac{{\delta }_a}{{\delta }_w}=\frac{(\frac{3}{2}-1)}{[\frac{\left(\frac{3}{2}\right)}{\left(\frac{4}{3}\right)}-1]}$

or, $\frac{{\delta }_a}{{\delta }_w}=\frac{\left(\frac{1}{2}\right)}{\left(\frac{1}{8}\right)}$

$\therefore \frac{{\delta }_a}{{\delta }_w}=4$

So, the ratio is $4:1$

$\begin{array}{c}\text{Why this question}?\\ \text{Tip: While applying the formula for deviation by thin prism}\\ \text{always take care to use relative refractive index.}\end{array}$