Question

A ray of light is incident normally on one refracting surface of an equilateral prism. If the refractive index of the material of the prism is 1.5, then

• A. the emergent ray is deviated by \(30^\circ\)
• B. the emergent ray is deviated by \(60^\circ\)
• C. the emergent ray just graces the second reflecting surface
• D. the ray undergoes total internal reflection at second refracting surface
• E. the ray emerges normally from the second refracting surface

Hint:

Normal incidence → no deviation; check TIR using critical angle.

Answer 1

The Correct Option is D

Concept: In a prism:
• If light is incident normally, it enters without deviation.
• Angle inside prism depends on prism geometry.
• Total internal reflection occurs if angle of incidence \(> \) critical angle.

Step 1: Understand prism geometry.
For an equilateral prism: \[ A = 60^\circ \]

Step 2: Ray enters normally.
Since incidence is normal: \[ i_1 = 0^\circ \Rightarrow r_1 = 0^\circ \] Thus ray travels undeviated inside prism.

Step 3: Angle at second face.
Inside prism: \[ r_1 + r_2 = A \Rightarrow 0 + r_2 = 60^\circ \] \[ r_2 = 60^\circ \]

Step 4: Find critical angle.
\[ \sin C = \frac{1}{\mu} = \frac{1}{1.5} = \frac{2}{3} \] \[ C \approx 41.8^\circ \]

Step 5: Compare angles.
\[ r_2 = 60^\circ > C = 41.8^\circ \]

Step 6: Conclusion.
Since angle of incidence at second surface is greater than critical angle: \[ \text{Total Internal Reflection occurs} \] \[ \boxed{\text{(D)}} \]