← Curved mirrors

Principal ray: parallel to the axis

Ivor has the mirror, the reference line, and the focal point drawn. Now he needs reflected paths. Measuring the angle at a curved surface for every single ray would take all day.

Three special beams have reflections you can draw without measuring anything. This lesson states the first rule of that toolkit: the beam that arrives parallel.

Take one beam heading for a concave mirror, running parallel to the reference line of the drawing.

The last lessons showed where such beams go after reflection: through the focal point.

principal axisfocal point
Concave: parallel in, through the focal point out.
The parallel ray rule, first half: a ray arriving parallel to the principal axis reflects through the focal point of a concave mirror.
The same rule covers the convex mirror: a ray arriving parallel to the principal axis reflects directly away from the virtual focal point.

Directly away means the reflected ray lies on the straight line from the virtual focal point through the strike point, heading outward.

principal axisvirtual focal point
Convex: parallel in, directly away from the virtual focal point out.

The rule holds for every parallel ray: high or low, near the axis or far from it.

principal axisfocal point
High or low, every parallel ray reflects through the same focal point.

One ruler line is all it takes. No angle is measured.

A ray arrives at a concave mirror parallel to the principal axis, striking the mirror high above the axis. Where does its reflection go?

The ray arrived parallel to the principal axis.

The parallel ray rule sends its reflection through the focal point.

So the reflected ray runs from the strike point through the focal point.

The reflected ray passes through the focal point.

A ray arrives at a convex mirror parallel to the principal axis. Where does its reflection go?

On a convex mirror, the parallel ray rule uses the virtual focal point behind the mirror.

The reflected ray heads directly away from that point.

Its dashed traced-back line passes through the virtual focal point.

The reflected ray heads directly away from the virtual focal point, its dashed trace-back passing through it.

A ray arrives at a concave mirror parallel to the principal axis. Where does the reflected ray go?

A ray arrives at a convex mirror parallel to the principal axis. Which describes the reflected ray?

Lennart says: 'On a ray diagram, a ray arriving parallel to the principal axis of a concave mirror reflects through the focal point.' Is Lennart correct?

Your turn

Which of the following states the parallel ray rule for curved mirror diagrams?

A ray arrives at a concave mirror parallel to the principal axis, far above the axis near the mirror's top edge. Where does its reflection go?

On a finished concave mirror diagram, one reflected ray passes through the focal point. Which incoming ray produced it?