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When red light in vacuum is incident at the Brewster angle on a certain glass slab, the angle of refraction is32 .What are (a) the index of refraction of the glass and (b) the Brewster angle?

Short Answer

Expert verified
  1. Theindex of refraction of glassis 1.60.
  2. Brewster angle is58.

Step by step solution

01

Listing the given quantities

Angle of refraction,r=32

02

Understanding the concepts of Brewster’s law

We use the formula for Brewster angle to find the refractive index of glass. The addition of Brewster angle and the angle of refraction is90.Using this concept, we can find the angle of refraction.

Formulae:

B=tan-1n2n1

B+r=90

03

(a) Calculations of the index of refraction of glass

The addition of Brewster angle and the angle of refraction is 90, i.e.B+r=90,

We haver=32.

Therefore,

B+32=90B=581

TheBrewster angle given by equation 33-49is

B=tan-1n2n1

If the incident and reflected rays travel in air, we can approximaten1as unity and letnbe the refractive index of the second medium. Then we have

B=tan-1nnglass=tanB=tan58=1.60

Hence, the index of refraction of glass is 1.60.

04

(b) Calculations of the Brewster angle

As calculated in part a), from equation (1), we can say that the Brewster angle is58.

Hence, Brewster angle is58.

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Figure:

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