Assume ABCD to be the rectangular glass slab with sides AB parallel to CD.

Let the refractive index of air and glass be n1and n2.

Consider a ray of light EF incident on surface AB of the glass slab with angle of incidence, ∠i.
The light ray is refracted into the glass slab along the path FG and towards the normal, NN’ . ∠ r1 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 is ∠r2.

The light ray emerges out of the slab forming ∠e as angle of emergence.

The surfaces AB and CD are parallel and FG is the transversal,
Therefore,  ∠r​1= ∠r1

Applying Snell’s Law at the surface AB,
sin isin r1=n2n1 .......(1)
Similarly, at surface CD, according to Snell’s Law
sin r2sin e=n1n2 .......(2)
Multiplying equation 1 and 2,

sin isin r1×sin r2sin e=n2n1×n1n2sin isin r1×sin 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 =  r2 
Hence,
sin isin r1×sin r1sin e=1sin isin e=1Therefore, sin i=sin eor, i=e

Hence, angle of incidence equals angle of emergence.

You Can Draw the figure by Yourself as it is not uploading . Hope it helps .

One more reason is that when light enters from the refractive index of air to the refractive index of Glass it refracts and again when it enters into the refractive index of air it will surely obtain the parallel path to the emergent ray .

The angle of incidence is the angle at which a ray of light strikes a surface, while the angle of emergence is the angle at which the same ray of light leaves the surface. In a rectangular glass slab, it can be proved that the angle of incidence is equal to the angle of emergence. This phenomenon is known as the law of reflection.



When a ray of light enters a rectangular glass slab, it undergoes refraction, which means that its direction changes. This change in direction occurs because the speed of light is different in air and in glass. As a result, the light ray bends towards the normal, which is a line perpendicular to the surface of the glass slab at the point of incidence.

When the light ray emerges from the glass slab, it undergoes refraction again, but this time it bends away from the normal. This is because the speed of light is different in glass and in air. The angle of emergence is the angle between the emergent ray and the normal.



To prove that the angle of incidence is equal to the angle of emergence in a rectangular glass slab, we can use the following steps:

1. Draw a diagram of a rectangular glass slab with an incident ray and an emergent ray.
2. Draw the normal to the surface of the glass slab at the point of incidence.
3. Measure the angle of incidence between the incident ray and the normal.
4. Measure the angle of refraction between the refracted ray and the normal.
5. Measure the angle of emergence between the emergent ray and the normal.
6. Compare the angle of incidence with the angle of emergence.

It can be observed that the angle of incidence is equal to the angle of emergence. This is because the angle of refraction is the same for both the incident and emergent rays, due to the symmetry of the glass slab.



In conclusion, the law of reflection states that the angle of incidence is equal to the angle of emergence in a rectangular glass slab. This is due to the symmetry of the glass slab, which ensures that the angle of refraction is the same for both the incident and emergent rays. This law is fundamental to the study of optics and has many practical applications, such as in the design of lenses and mirrors.