Question

Two rays of light A and B are falling on a glass slab at the angles of incidence 45° and 60°. if the reflected ray of A is partially polarized and that of B is completely polarized, then the refractive index of glass is

• A. 1.33
• B. 1.414
• C. 1.5
• D. 1.65
• E. 1.732

Answer 1

Answer: (E)

When light is reflected from a surface, the reflected ray is completely polarized at the Brewster's angle. The Brewster's angle \(\theta_B\) is given by the relation: \[ \tan(\theta_B) = n \] where \(n\) is the refractive index of the material. For ray B to be completely polarized, the angle of incidence must be the Brewster's angle. For ray B, the angle of incidence is \(60^\circ\). Therefore, \[ \tan(60^\circ) = n \] We know that \(\tan(60^\circ) = \sqrt{3}\). Hence, \[ n = \sqrt{3} \approx 1.732 \]

So, the correct option is (E) : \(1.732\)

Answer 2

For a ray to be completely polarized after reflection, it must satisfy Brewster’s law, which states:

\(\mu = \tan \theta_B\) 

where:
    \(\mu\) = refractive index of glass
    \(\theta_B\) = Brewster’s angle

In the given question, ray B is completely polarized at an angle of incidence of 60°. So,

\(\mu = \tan 60^\circ = \sqrt{3} = 1.732\)

Correct Option: 1.732