Question

The refractive index of the material of a glass prism is \( 3 \). The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism?

• A. 50°
• B. 60°
• C. 58°
• D. 48°

Hint:

For prisms, when the angle of minimum deviation equals the angle of the prism, use the relation involving the refractive index to calculate the angle of the prism.

Answer 1

The Correct Option is B

When the refractive index of prism material is provided and the angle of minimum deviation equals the prism's angle, the angle of the prism is determined using the prism's angle of deviation formula.

The formula connecting refractive index (\( n \)), prism angle (\( A \)), and minimum deviation angle (\( \delta_m \)) is:

\(n = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)}\)

Given values:

• Refractive index, \( n = 3 \)
• Angle of minimum deviation, \( \delta_m = A \)

Substituting \( \delta_m = A \) into the formula yields:

\(n = \frac{\sin(A)}{\sin\left(\frac{A}{2}\right)}\)

With \( n = 3 \), the equation becomes:

\(3 = \frac{\sin(A)}{\sin\left(\frac{A}{2}\right)}\)

The objective is to find the angle \( A \) that satisfies this equation.

Solving this equation through trigonometric identities and known values reveals:

\(A = 60^\circ\)

This result aligns with the given options, confirming the prism angle is 60°.

Consequently, the correct answer is 60°.