Question

A ray of light travelling through glass of refractive index \( \sqrt{2} \) is incident on glass-air boundary at an angle of incidence 45°. If refractive index of air is 1, then the angle of refraction will be

• A. 30°
• B. 90°
• C. 60°
• D. 45°

Hint:

For total internal reflection, the angle of refraction becomes 90° at the critical angle. Use Snell's law to calculate the refraction angle.

Answer 1

The Correct Option is B

Step 1: Using Snell's Law.
Snell's law states: \[ n_1 \sin \theta_1 = n_2 \sin \theta_2 \] where \( n_1 \) and \( n_2 \) are the refractive indices of the two mediums, and \( \theta_1 \) and \( \theta_2 \) are the angles of incidence and refraction, respectively.
Step 2: Applying the values.
In this case, \( n_1 = \sqrt{2} \), \( n_2 = 1 \), and \( \theta_1 = 45^\circ \). Using Snell's law: \[ \sqrt{2} \sin 45^\circ = 1 \sin \theta_2 \] Since \( \sin 45^\circ = \frac{1}{\sqrt{2}} \), we get: \[ \sqrt{2} \times \frac{1}{\sqrt{2}} = \sin \theta_2 \] \[ 1 = \sin \theta_2 \] \[ \theta_2 = 90^\circ \]
Step 3: Conclusion.
The angle of refraction is \( 90^\circ \), so the correct answer is (B).