Question

The exit surface of a prism with refractive index $n$ is coated with a material having refractive index $\dfrac{n}{2}$. When this prism is set for minimum angle of deviation, it exactly meets the condition of critical angle. The prism angle is ___.

• A. $30^\circ$
• B. $60^\circ$
• C. $15^\circ$
• D. $45^\circ$
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Hint:

At minimum deviation, internal refraction angles in a prism are equal and symmetric.

Answer 1

The Correct Option is B

Step 1: Applying the condition for minimum deviation.
At minimum deviation, the ray travels symmetrically inside the prism and the angle of refraction at each face is equal.
Step 2: Using the critical angle condition.
Critical angle $C$ is given by:
\[ \sin C = \dfrac{n/2}{n} = \dfrac{1}{2} \] \[ C = 30^\circ \] Step 3: Relating prism angle and refraction angle.
At minimum deviation:
\[ A = 2r \] Here, $r = C = 30^\circ$.
Step 4: Calculating the prism angle.
\[ A = 2 \times 30^\circ = 60^\circ \] Step 5: Final conclusion.
The prism angle is $60^\circ$, corresponding to option (2).