Question

An unpolarised light is incident on a glass slab such that the reflected ray is totally polarised. If the angle of refraction is 30°,the refractive index of the glass is:

• A. 1.5
• B. 1.73
• C. 1.41
• D. 1.45
• E. 1.6

Answer 1

The Correct Option is B

The correct answer is (B): 1.73

Answer 2

To find the refractive index of the glass, we can use Brewster's Law, which states that the reflected light is completely polarized when the angle of incidence \( \theta_B \) (Brewster's angle) satisfies the following relationship:

\[ \tan \theta_B = n \]

where \( n \) is the refractive index of the glass with respect to air.

Brewster's angle is related to the angle of refraction \( \theta_r \) through Snell's Law. Since the angle of refraction \( \theta_r \) is given as 30°, we can use this information to find the refractive index.

First, we recall that Brewster's angle \( \theta_B \) and the angle of refraction \( \theta_r \) are complementary when the reflected ray is completely polarized. This means:

\[ \theta_B + \theta_r = 90^\circ \]

Given \( \theta_r = 30^\circ \):

\[ \theta_B = 90^\circ - 30^\circ = 60^\circ \]

Now, we can apply Brewster's Law:

\[ \tan \theta_B = \tan 60^\circ = n \]

We know that:

\[ \tan 60^\circ = \sqrt{3} \]

Therefore, the refractive index of the glass is:

\[ n = \sqrt{3} \]

So, the refractive index of the glass is \( \sqrt{3} \) or approximately 1.732.
So The correct answer is Option (B): 1.73