An equilateral prism is made of material of refractive index $\sqrt{3}$. Angle of minimum deviation through the prism is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 60°
To calculate the angle of minimum deviation,
Refractive index, $μ=\frac{\sin\left(\frac{A+δ_{min}}{2}\right)}{\sin\left(\frac{A}{2}\right)}$
for an equilateral prism: $A=60°$
$⇒\sin\left(\frac{A+δ_{min}}{2}\right)=μ\sin\left(\frac{A}{2}\right)$
$⇒\sin\left(\frac{A+δ_{min}}{2}\right)=\sqrt{3}×\frac{1}{2}=\frac{\sqrt{3}}{2}$
$⇒\frac{A+δ_{min}}{2}=60°$
$⇒δ_{min}=120-A=60°$