Physics - Geometrical Optics Question with Solution | TestHub

For a thin prism, the angle of minimum deviation is given by $\delta =(\mu -1)A$, where $\mu$ is the refractive index of the prism relative to the surrounding medium and $A$ is the angle of the prism.

In air, the deviation is:

${\delta }_1=({\mu }_g-1)A=\left(\frac{3}{2}-1\right)A=\frac{A}{2}$

When the prism is immersed in water, the refractive index of glass relative to water is:

${\mu }_{gw}=\frac{{\mu }_g}{{\mu }_w}=\frac{3/2}{4/3}=\frac{9}{8}$

The deviation in water is:

${\delta }_2=({\mu }_{gw}-1)A=\left(\frac{9}{8}-1\right)A=\frac{A}{8}$

Taking the ratio of ${\delta }_2$ to ${\delta }_1$:

$\frac{{\delta }_2}{{\delta }_1}=\frac{A/8}{A/2}=\frac{1}{4}$

${\delta }_2=\frac{{\delta }_1}{4}$

Answer: $\frac{{\delta }_1}{4}$