Question

An equilateral prism is made of material of refractive index \(\sqrt{3}\). The angle of minimum deviation through the prism is:

• A. \(60\degree\)
• B. \(30\degree\)
• C. \(45\degree\)
• D. \(0\degree\)

Answer 1

The Correct Option is B

For minimum deviation (δₘ):

\[ \mu = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)} \]

\[ \sqrt{3} = \frac{\sin\left(\frac{60° + \delta_m}{2}\right)}{\sin(30°)} \]

\[ \sqrt{3} \times \frac{1}{2} = \sin\left(30° + \frac{\delta_m}{2}\right) \]

\[ \frac{\sqrt{3}}{2} = \sin\left(30° + \frac{\delta_m}{2}\right) \]

\[ \Rightarrow 30° + \frac{\delta_m}{2} = 60° \]

\[ \frac{\delta_m}{2} = 30° \]

\[ \delta_m = 60° \]