Question

The refractive index of the material of an equilateral prism is $1.6$. The angle of minimum deviation due to the prism would be

• A. 30°
• B. between 30° and 45°
• C. 45°
• D. between 45° and 60°

Answer 1

Answer: (D)

$A=60^{\circ }$
$\mu =1.6$
$\mu =\frac{\sin \left(\frac{A+\delta \min }{2}\right)}{\sin A/2}\delta \min$
$1.6=\frac{\sin \left(\frac{60+8\min }{2}\right)}{\sin 30^{\circ }}$
$\sin \left(\frac{60+8\min }{2}\right)=1.6\times \frac{1}{2}=0.8$
${\sin }^{-1}(0.8)=53.10^{\circ }$
$\frac{60+\delta \min }{2}=53.10^{\circ }$
$\delta \min =\frac{53.10\times 2}{60}=1.77^{\circ }$