Question

Refractive index of prism is \( \sqrt{2} \). What should be the angle of incidence for a light ray such that the emerging ray grazes out of the surface?

• A. 90°
• B. 60°
• C. 30°
• D. 45°

Hint:

The angle of incidence for a grazing ray in a prism should be equal to the critical angle, where \( \sin \theta_c = \frac{1}{n} \).

Answer 1

The Correct Option is A

Step 1: Understanding the problem.
In this question, we are dealing with a prism with a refractive index \( n = \sqrt{2} \), and we need to find the angle of incidence such that the emerging ray grazes out of the surface of the prism. Grazing out of the surface implies that the angle of refraction at the second surface of the prism is 90°, meaning the light ray is just refracted along the surface.
Step 2: Using the formula for the critical angle.
The critical angle \( \theta_c \) is the angle of incidence at the surface of the prism beyond which total internal reflection occurs. The condition for the grazing ray can be related to the refractive index using the formula: \[ \sin \theta_c = \frac{1}{n} \] where \( n = \sqrt{2} \). Substituting the values: \[ \sin \theta_c = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2} \] So, the critical angle is: \[ \theta_c = 45^\circ \]
Step 3: Angle of incidence.
In a prism, the angle of incidence at the first surface must be equal to the critical angle for the light to graze out of the surface. Therefore, the angle of incidence required for the ray to graze out is: \[ \theta = 90^\circ \] Hence, the correct answer is 90°.