Question

Find the angle of minimum deviation for an equilateral prism made of a material of refractive index 1.732. What is the angle of incidence for this deviation ?

Answer 1

$\mu =\frac{sin\left[\frac{{\delta }_{min}+A}{2}\right]}{sin\left[\frac{A}{2}\right]}A={60}^{\circ }$

$\Rightarrow \sqrt{3}\times sin\left({30}^{\circ }\right)=sin\left(\frac{{\delta }_{min}+{60}^{\circ }}{2}\right)$

$\Rightarrow \frac{\sqrt{3}}{2}=sin\left(\frac{{\delta }_{min}+{60}^{\circ }}{2}\right)$

$\Rightarrow \left(\frac{{\delta }_{min}+{60}^{\circ }}{2}\right)={60}^{\circ }$

${\delta }_{min}={60}^{\circ }$

${\delta }_{min}=2i-A$

$2i={120}^{\circ }$

$i={60}^{\circ }$