Question

The refractive index of the material of an equilateral prism is √2. The angle of minimum deviation of the prism is______.
Fill in the blank with the correct answer from the options given below.

• A. 30°
• B. 75°
• C. 60°
• D. 90°

Answer 1

The Correct Option is A

The angle of minimum deviation (\(D\)) for a prism can be found using the prism formula:
\( n = \frac{\sin((A + D)/2)}{\sin(A/2)} \)
where \(n\) is the refractive index and \(A\) is the prism angle.
Given: \(n = \sqrt{2}\) and for an equilateral prism, \(A = 60^\circ\).
We want to find \(D\).
Given the equation:
\( \sqrt{2} = \frac{\sin((60^\circ + D)/2)}{\sin(60^\circ/2)} \)
Calculating \(\sin(30^\circ)\) gives \( \frac{1}{2} \).
So, \(\sqrt{2} = 2\sin((60^\circ + D)/2)\).
This implies:
\(\sin((60^\circ + D)/2) = \frac{\sqrt{2}}{2} = \sin(45^\circ)\).
Thus:
\((60^\circ + D)/2 = 45^\circ\).
Solving for \(D\):
\(60^\circ + D = 90^\circ\).
\(D = 90^\circ - 60^\circ\).
\(D = 30^\circ\).
Thus, the angle of minimum deviation is 30°.