Physics

Physics

Problem

An incident ray makes an angle α\alpha with the surface of a plane mirror. Derive an expression for the angle between the incident and reflected rays in terms of α\alpha.
Intuitive explanation

The key is to remember that angles in optics are measured from the normal (perpendicular to the surface), not from the surface itself. If the incident ray makes angle α\alpha with the surface, it makes angle (90°−α)(90° - \alpha) with the normal. By the law of reflection, the reflected ray makes the same angle with the normal on the opposite side. Draw both rays and use geometry to find the angle between them—you'll see they form a triangle with the normal as a reference line.

Intuitive explanation

The key is to remember that angles in optics are measured from the normal (perpendicular to the surface), not from the surface itself. If the incident ray makes angle α\alpha with the surface, it makes angle (90°−α)(90° - \alpha) with the normal. By the law of reflection, the reflected ray makes the same angle with the normal on the opposite side. Draw both rays and use geometry to find the angle between them—you'll see they form a triangle with the normal as a reference line.

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