The refractive index of an equilateral prism is $\sqrt{3}$. The angle of incidence for which angle of deviation is minimum is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 60°
Relationship between the refraction index (μ) of the material and angle of minimum deviation -
$μ=\frac{\sin\left(\frac{A+S_{min}}{2}\right)}{\sin\left(\frac{A}{2}\right)}$
In equilateral prism, Angle of Prism (A) = 60°
$μ=\sqrt{3}$ [given]
$\sqrt{3}=\frac{\sin\left(\frac{60°+S_{min}}{2}\right)}{\sin\left(\frac{60°}{2}\right)}$
$\sqrt{3}=2\sin\left(\frac{60°+S_{min}}{2}\right)$
$⇒\frac{60°+S_{min}}{2}=\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)$
$⇒\frac{60°+S_{min}}{2}=60°$
$⇒S_{min}=60°$