Reflection & Plane Mirrors
Why your reflection seems to stand as far behind the mirror as you stand in front.
Lesson at a glanceShow the key points
- Laws of reflection: angle of incidence = angle of reflection; incident ray, reflected ray and normal are coplanar.
- Rays from a point object reflected by a plane mirror all seem to diverge from one point behind it: the virtual image.
- Congruent triangles show the image is as far behind the mirror as the object is in front (SA = AI).
- On a curved surface the laws hold at each point, using the normal to the tangent plane there.
Light’s wavelength is tiny compared with mirrors, lenses and the things we look at, so diffraction can usually be ignored and light treated as straight rays. That is geometrical optics, and it starts with the humble mirror.
The laws of reflection
A ray of light striking a smooth surface is reflected so that
- the angle of incidence equals the angle of reflection (both measured from the normal), and
- the incident ray, the reflected ray and the normal all lie in one plane.
The image in a plane mirror
Put a point source S in front of a flat mirror. A ray SA striking the mirror at right angles comes straight back. Another ray SB, striking at angle i, reflects along BC. Extend AS and BC behind the mirror: they meet at a point I. Using the law of reflection, the triangles SAB and IAB are congruent, so SA = AI. Every reflected ray, extended backwards, passes through the same point I.
An eye receiving the reflected rays can’t tell where they really came from; they seem to diverge from I. So I is the image of S. No light actually passes through I, so it is a virtual image.
You stand 3.0 m from a wall mirror and walk 1.0 m toward it. How far are you from your image now, and how much did that distance change?
Curved surfaces
The same laws work for a curved mirror, point by point. At the point where a ray strikes, imagine the plane just touching the surface (the tangent plane) and draw the normal perpendicular to it. The angles of incidence and reflection are measured from that normal.
- 1Angle of incidence = angle of reflection; incident ray, reflected ray and normal are coplanar.
- 2A plane mirror forms a virtual image as far behind it as the object is in front (SA = AI).
- 3On curved mirrors the laws hold at each point, using the normal to the tangent plane.
Check yourself
Keep exploring
Hand-picked videos, simulations and readings that explain this idea from a different angle.