Question

Prove the statement.

 If the angle of incidence and angle of emergence of a light ray falling on a glass slab are i and e respectively, prove that, i = e.

Answer 1

Let \[\mu\] be the refractive index of the glass slab.  Then, according to Snell's law,

\[\frac{\sin i}{\sin r_1} = \mu\]      .....(i) 

and

\[\frac{\sin r_2}{\sin e} = \frac{1}{\mu}\]   .....(ii)

But, r₁ = r₂   .....(iii)
Putting (iii) in (i), we have

\[\frac{\sin r_2}{\sin e} = \mu\]      .....(iv)
Multiplying (i) and (iv), we have

\[\frac{\sin i}{\sin e} = 1\]
or
\[i = e\] 

Answer 2

Light is travelling from air to glass.

where,

i = Angle of incidence

r = Angle of refraction

e = Angle of emergency

∴ _gn_a = `1/(""_"a""n"_"g")`  .....(i)

At surface PQ

_gn_a = `(sin "i")/(sin "r")`  .....(ii)

At surface SR

_an_g = `(sin "r")/(sin "e")`  ....(iii)

Substituting (ii) and (iii) in (i)

`(sin "i")/(sin "r") = 1/((sin "r")/(sin "e"))`

∴ `(sin "i")/(sin "r") = (sin "e")/(sin "r")`

∴ sin i = sin e

∴ i = e