Question

How is can we prove that angle of reflection = angle of incidence?

Answer 1

Light always travel the smallest time path. If light has to travel from one point to another, it will take that path by which it will reach to another point in the smallest possible time.
Light is known to behave in a very predictable manner. If a ray of light could be observed approaching and reflecting off of a flat mirror, then the behavior of the light as it reflects would follow a predictable law known as the law of reflection. The diagram below illustrates the law of reflection.

In the diagram, the ray of light approaching the mirror is known as the incident ray (labeled I in the diagram). The ray of light that leaves the mirror is known as the reflected ray (labeled R in the diagram). At the point of incidence where the ray strikes the mirror, a line can be drawn perpendicular to the surface of the mirror. This line is known as a normal line (labeled N in the diagram). The normal line divides the angle between the incident ray and the reflected ray into two equal angles. The angle between the incident ray and the normal is known as the angle of incidence. The angle between the reflected ray and the normal is known as the angle of reflection.

The law of reflection states that when a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection.

To view an image of a pencil in a mirror, you must sight along a line at the image location. As you sight at the image, light travels to your eye along the path shown in the diagram below. The diagram shows that the light reflects off the mirror in such a manner that the angle of incidence is equal to the angle of reflection.

If angle of incident ray is not equal to angle of reflected ray than you won't be able to see the image of the object in a mirror.