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

in figure. PQ || SR
NM is a refracted ray. ∴ 𝑟= 𝑖₁
By the laws of refraction, 
_𝑔𝑛_𝑎= `(sin i)/(sin r) ;  _a n_g= (sin i _1)/(sin_e)`
` therefore  _g n_a  = 1 / (" _a n_g) ` 
∴ `(sin i)/(sin r)  = (sin e)/(sin i _1)    .......but  r=i_1`
∴  sin 𝑖 = sin 𝑒
∴  𝑖 = 𝑒