Physics - Geometrical Optics Question with Solution | TestHub

The formula to calculate the refractive index $\left(\mu \right)$ of the material of the prism is given by

$\mu =\frac{\sin \left({\displaystyle \frac{A+{\delta }_m}{2}}\right)}{\sin \left({\displaystyle \frac{A}{2}}\right)} ...\left(1\right)$

From equation (1), it follows that

$\cot \frac{A}{2}=\frac{\sin \left(\frac{A+{\delta }_m}{2}\right)}{\sin \frac{A}{2}}$

$$\begin{gathered} \Rightarrow \cos \frac{A}{2}=\sin \left(\frac{A+{\delta }_m}{2}\right) \\ \Rightarrow \sin \left(\frac{\pi }{2}-\frac{A}{2}\right)=\sin \left(\frac{A+{\delta }_m}{2}\right) \end{gathered}$$

$\Rightarrow \frac{\mathrm{A}+{\delta }_m}{2}=\frac{\pi }{2}-\frac{\mathrm{A}}{2}$

$\Rightarrow {\delta }_m=\pi -2 \mathrm{A}$