Question

An unpolarised light is incident at an interface of two dielectric media having refractive indices of $2$ (incident medium) and $2\sqrt{3}$ (refracted medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is ___.

• A. $45^\circ$
• B. $30^\circ$
• C. $10^\circ$
• D. $60^\circ$

Hint:

If reflected and refracted rays are perpendicular, the angle of incidence is equal to the Brewster angle.

Answer 1

The Correct Option is D

Step 1: Using the condition for perpendicular reflected and refracted rays.
When reflected and refracted rays are perpendicular to each other, the angle of incidence equals the Brewster angle.
Step 2: Applying Brewster’s law.
\[ \tan i_B = \dfrac{n_2}{n_1} \] Step 3: Substituting the given refractive indices.
\[ \tan i_B = \dfrac{2\sqrt{3}}{2} = \sqrt{3} \] Step 4: Determining the angle of incidence.
\[ i_B = 60^\circ \] Step 5: Final conclusion.
The angle of incidence is $60^\circ$, corresponding to option (4).