Question

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. Prove the statement

Answer 1

Angle of Incidence means the angle by which light is hitting on the surface and get reflected to some angle.

Refer to the Attachment 

Let ABCD is the glass slab
Assume that the air Index and glass index = n₁ and n₂
From the diagram , 
Consider a light ray WX makes the ∠i on the surface AB.
Reflected light XY to the Normal NN' makes the angle   ∠r₁
Refracted light YZ outside the slab CD makes the angle ∠₂
Here we observe that AB and CD are parallel and XY is transversel.

Applying snell  law on first surface (AB) & CD we get simultaneously 

$\frac{sin i}{sinr_{1}} = \frac{n_{2}}{n_{1}}$ -----→(a)

$\frac{sin r_{2}}{sin_{e}} = \frac{n_{1}}{n_{2}}$----→(b)

On multiplying eq. (a) & (b) , we get

$\frac{sini}{sinr_{1}} * \frac{sinr_{1}}{sine}$ 
or $\frac{sini}{sine} = 1$ 
Hence,
sin i = sin e 

∴  $\boxed{i = e}$ 

Hence proved.


Hope it Helps :-)

Answer 2

Answer:

Let ABCD is the glass slab

Assume that the air Index and glass index = n₁ and n₂

From the diagram , 

Consider a light ray WX makes the ∠i on the surface AB.

Reflected light XY to the Normal NN' makes the angle   ∠r₁

Refracted light YZ outside the slab CD makes the angle ∠₂

Here we observe that AB and CD are parallel and XY is transversel.

Applying snell  law on first surface (AB) & CD we get simultaneously 

-----→(a)

----→(b)

On multiplying eq. (a) & (b) , we get

 

or  

Hence,

sin i = sin e