Question

In an equilateral prism the path of a ray is shown in the figure. Determine the refractive index of the prism.

• A. \(1.71\)
• B. \(1.52\)
• C. \(1.39\)
• D. \(1.84\)

Hint:

For equilateral prism problems: \[ A = 60^\circ \] and always use \[ r_1 + r_2 = A \] before applying Snell's law.

Answer 1

The Correct Option is A

Concept: For an equilateral prism, \[ A = 60^\circ \] Using prism geometry: \[ r_1 + r_2 = A \] Snell's law at first surface: \[ \mu = \frac{\sin i}{\sin r_1} \] Step 1: Determine refracted angles from geometry.} From the diagram the ray strikes the base normally, therefore \[ r_2 = 30^\circ \] Thus \[ r_1 = 60^\circ - 30^\circ = 30^\circ \] Step 2: Use Snell's law at first surface.} The incident ray makes \(60^\circ\) with the normal. \[ \mu = \frac{\sin 60^\circ}{\sin 30^\circ} \] \[ \mu = \frac{\sqrt{3}/2}{1/2} \] \[ \mu = \sqrt{3} \] \[ \mu \approx 1.73 \] \[ \mu \approx 1.71 \]