Question

A monochromatic ray of light is incident at an angle of \( 45^\circ \) on the face AB of a right-angled prism (\( A = 90^\circ \)), as shown in the figure. The emergent ray is refracted tangentially from the face AC. Find out the refractive index of the prism material. 

Hint:

At the critical angle, light refracts tangentially along the interface.

Answer 1

Applying Snell's law at face AB: \[ n_{\text{air}} \sin 45^\circ = n_{\text{prism}} \sin r \] Since \( r = 90^\circ \), the critical angle condition applies: \[ \sin 45^\circ = \frac{1}{n} \] \[ n = \frac{1}{\sin 45^\circ} \] \[ n = \frac{1}{\frac{1}{\sqrt{2}}} = \sqrt{2} \] \[ \boxed{n = 1.414} \]