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

(A) 45°

(B) 60°

(C) 10°

(D) 30°

Correct Answer: 60°

Explanation (Complete Calculation)

When the reflected ray and refracted ray are perpendicular to each other, the condition of Brewster’s angle is satisfied.

At Brewster angle:

\[ i + r = 90^\circ \]

According to Brewster’s law, the tangent of the angle of incidence is equal to the ratio of refractive indices of the two media:

\[ \tan i = \frac{n_2}{n_1} \]

Here, refractive index of incident medium:

\[ n_1 = 2 \]

Refractive index of second medium:

\[ n_2 = 2\sqrt{3} \]

Substitute the values:

\[ \tan i = \frac{2\sqrt{3}}{2} \]
\[ \tan i = \sqrt{3} \]

The angle whose tangent is \(\sqrt{3}\) is:

\[ i = 60^\circ \]

Hence, the required angle of incidence is 60°.

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