Question

2. A ray of light travelling through air falls on the surface of a glass slab and emerges out of it parallel to the<br />incident ray. The angle of incidence i, angle of refraction in glass r and angle of emergence is e. Find the ratio of sin i/sin e and refraction index of glass in terms of e and r .
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Answer 1

Answer:

Asume ABCD a glass plate with side AB parallel to CD

Let refractive index of air and glass is n1 and n2

Consider a ray of light EF incident on

surface AB of the glass slab with angle

of incidence.,4i.

The light ray is refracted into the glass

slab along the path FG and towards the

normal, NN' .2 r is the angle of

refraction.

The light ray is refracted out of the

glass slab at the surface CD along the

path GH. The angle of incidence at this

surface <r2The light ray emerges out of the slab

forming Ze as angle of emergence.

The surfaces AB and CD are parallel

and FG is the transyersal,

Therefore, r1 1

Applying Snell's Law at the surface AB,

sin isin r1-n2n1..

Similarly, at surface CD, according to

Snell's Law

sin r2sin e-n1n2..

Multiplying equation 1 and 2,

sin isin r1xsin r2sin e-n2n1xn1n2sin isin

r1xsin r2sin e1

Ore, Sin l-SIn eor, 1-

Hence, angle of incidence equals angle

of emergence.

r1xsin r2sin e-1

As AB is parallel to CD, the

perpendiculars to the AB and CD, NN'

and MM' are also parallel

Therefore, alternate interior angles,

r1 and r2are congruent i.e. r1

Hence.

sin isin r1xsin r1sin e-1sin isin e-1Theref