Question

A right-angled prism ABC (refractive index \( \sqrt{2} \)) is kept on a plane mirror as shown in the figure. A ray of light is incident normally on the face AC. Trace the path of the ray as it passes through the prism.

Answer 1

Ray Path Through a Prism

Parameters Provided:

• Prism refractive index: \( n = \sqrt{2} \)
• Prism angle: \( A = 90^\circ \)
• Angle of incidence on face AC: \( 0^\circ \) (normal incidence)
• Angle \( \angle BAC = 60^\circ \)

The ray's progression is as follows:

1. Normal incidence on face AC results in an angle of incidence of \( 0^\circ \).
2. The ray traverses the prism without deviation until it encounters face AB.
3. Refraction occurs at the interface of the prism and air at face AB.

Snell's Law is applied at face AB to determine the angle of refraction:

\[ n_{\text{prism}} \sin \theta_1 = n_{\text{air}} \sin \theta_2 \]

Definitions:

• \( \theta_1 \) represents the angle within the prism.
• \( \theta_2 \) represents the angle of refraction in air.

Applying Snell's Law for light moving from the prism (refractive index \( \sqrt{2} \)) to air (refractive index 1):

\[ \sqrt{2} \sin \theta_1 = 1 \cdot \sin \theta_2 \]

This equation allows for the calculation of \( \theta_2 \), the angle of refraction in air.