Physics - Geometrical Optics Question with Solution | TestHub

Using prism formula, $\mu =\frac{\sin \left(\frac{\mathrm{A}+{\delta }_{\mathrm{m}}}{2}\right)}{\sin \left(\frac{\mathrm{A}}{2}\right)}$ ...(i) where, $A=$ angle of prism ${\delta }_{\mathrm{m}}=$ angle of minimum deviation Given, $\mu =\cot \left(\frac{\mathrm{A}}{2}\right)=\frac{\cos \left(\frac{\mathrm{A}}{2}\right)}{\sin \left(\frac{\mathrm{A}}{2}\right)}$ So, from Eq. (i) $\begin{array}{rl}& \frac{\cos \left(\frac{\mathrm{A}}{2}\right)}{\sin \left(\frac{\mathrm{A}}{2}\right)}=\frac{\sin \left(\frac{\mathrm{A}+{\delta }_{\mathrm{m}}}{2}\right)}{\sin \left(\frac{\mathrm{A}}{2}\right)}\\ \Rightarrow & \sin \left(\frac{\pi }{2}-\frac{\mathrm{A}}{2}\right)=\sin \left(\frac{\mathrm{A}}{2}+\frac{{\delta }_{\mathrm{m}}}{2}\right)\\ \Rightarrow & {\delta }_{\mathrm{m}}=\pi -2\mathrm{A}=180^{\circ }-2\mathrm{A}\end{array}$