Question

A ray of light travelling through air falls on the
surface of a glass slab and emerges out of it
parallel to the 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 refractive index of glass in terms of
e and r.

Answer 1

Answer:

Explanation:

Since, μ=speed of  light in medium/speed of  light in vacuum

μg=2×1083×108=1.5

r=90−i

Hence from Snell's law,μ1

sini=μ2

sinr 1sini=23

sin(90−i)tan i=23

i=tan−1(3/2)=56.30

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Answer 2

The ratio of sin i/sin r is 1

The refractive index of glass in terms of e and r is

Refractive index of the glass = sin e/sin r

Explanation:

If the refractive index of the glass slab is n then

by Snell's law

$n=\frac{\sin i}{\sin r}$   .......... (1)

Since both the normals are parallel therefore, the alternate angles will be equal

Therefore, $\theta=r$

Again when ray of light enters from glass slab to air

$\frac{1}{n}=\frac{\sin r}{\sin e}$   ......... (2)

Multiplying (1) and (2)

$n\times\frac{1}{n}=\frac{\sin i}{\sin r}\times \frac{\sin r}{\sin e}$

$\implies 1=\frac{\sin i}{\sin e}$

or, $\frac{\sin i}{\sin e}=1$

From (2)

Refractive index of glass in terms of e and r

$n=\frac{\sin e}{\sin r}$

Hope this answer is helpful.

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