Q.The angle of minimum deviation for the equilateral prism is 40°. Find the refractive index of the material of the prism.

Plotting deviation $d$ against angle of incidence $i_1$ for a prism gives a curve that falls to a single minimum value $D$ (the angle of minimum deviation) before rising again; at this minimum the ray path through the prism is symmetric, with the incident and emergent angles equal ($i_1=i_2=i$), the two internal refraction angles equal ($r_1=r_2=r=A/2$, since $r_1+r_2=A$), and the ray inside the prism running parallel to its base. Substituting $i_1=i_2=i$, $r_1=r_2=A/2$ and $i=(A+D)/2$ (from $D=2i-A$) into Snell's law $n=\sin i/\sin …