Question

A thin prism is made of a material having refractive indices $1.61$ and $1.65$ for red and violet lights, respectively. The dispersive power of the material is $\mathrm{0.07.}$ It is found that a beam of yellow light passing through the prism suffers a minimum deviation of $4^{\circ }$ in favourable conditions. The angle of prism is ${\theta }^{\circ }$. The value of $theta$ is (integer only)

Answer 1

Given,

${\mu }_r=1.61;{\mu }_v=1.65\omega =0.07;\delta y=4^{\circ }$

The dispersive power is,

$\omega =\frac{{\mu }_v-{\mu }_r}{{\mu }_y-1}$

$\Rightarrow 0.07=\frac{1.65-1.61}{{\mu }_y-1}$

$\Rightarrow {\mu }_y-1=\frac{0.04}{0.07}=\frac{4}{7}$

Let the angle of the prism be $A$.

Angle of minimum deviation is,

${\delta }_y=({\mu }_y-1)A$

$\Rightarrow A=\frac{{\delta }_y}{{\mu }_y-1}=\frac{4}{\left(\frac{4}{7}\right)}=7^{\circ }$

So, the angle of the prism is $7^{\circ }$.

Hence, $\theta =7$