A ray of light is refracted by a glass prism. Obtain an expression for the refractive index of the glass in terms of the angle of prism A and the angle of minimum deviation $\displaystyle \delta \mathrm{m}$.

Obtaining expression \[\mu=\frac{\sin \left(\dfrac{A+\delta_{\mathrm{m}}}{2}\right)}{\sin \left(\dfrac{A}{2}\right)} \] At minimum deviation, a ray of light passes through a prism symmetrically i.e \(\displaystyle \angle i=\angle e, \angle r_{1}=\angle r_{2}=\angle r\) We know that \(\displaystyle i+e=A+\delta \quad\) and \(\displaystyle r_{1}+r_{2}=A\) \[\begin{aligned} \therefore \quad & i+i=A+\delta \mathrm{m} \\ & i=\frac{A+\delta \mathrm{m}}{2} \end{aligned} \] And also \[\begin{aligned} & r+r=A \\ \Rightarrow & r=\frac{A}{2} \end{aligned} \] Using Snell's law \[\begin{aligned} & \mu=\frac{\sin i}{\sin r} \\ & \mu=\frac{\sin \left(\dfrac{A+\delta \mathrm{m}}{2}\right)}{\sin \left(\dfrac{A}{2}\right)} \end{aligned} \]