Laws of reflection

The idea

The angle of incidence equals the angle of reflection, and the incident ray, the normal at the point of incidence and the reflected ray lie in the same plane; these laws hold for all reflecting surfaces, including spherical ones.

Bounce off a mirror

A ray of light hits a mirror. The dashed line at right angles to the mirror is the normal. The ray makes an angle of 30° with the normal.

At what angle to the normal will the ray leave the mirror?

• 30°, on the other side of the normal
• 60°
• Along the mirror, without leaving it

Aim the torch

Plane mirror: drag the torch round the mirror and light each sensor with the reflected ray. Concave and convex mirrors: drag the spot where the ray hits the mirror, to the top and to the bottom.

Same angle, same plane

The angle of incidence is equal to the angle of reflection, and the incident ray, the normal to the mirror at the point of incidence and the reflected ray all lie in the same plane. These laws hold for all reflecting surfaces, including spherical ones.

Check the second law. A flat card stands on the mirror with all three lines drawn on it. Bend the right half back.

Both angles are measured from the normal, never from the mirror surface.

• Law | What you saw
• ∠i = ∠r | The sensor lit only when the torch angle matched the sensor angle
• Same plane | Bending the card took the reflected ray off it
• All surfaces | On the curved mirrors the normal turned from spot to spot, but ∠i = ∠r every time

Notes

The angle of incidence equals the angle of reflection, and the incident ray, the normal at the point of incidence and the reflected ray lie in the same plane; these laws hold for all reflecting surfaces, including spherical ones.

Check yourself

A ray strikes a plane mirror and makes an angle of 35° with the mirror surface (see the picture). What is the angle of reflection?

Answer: 55 °

The normal is at 90° to the surface, so ∠i = 90° − 35° = 55°. Then ∠r = ∠i = 55°.

A ray falls on a plane mirror with an angle of incidence of 25°. What is the angle between the incident ray and the reflected ray?

Answer: 50 °

∠i = 25° and ∠r = 25°. The rays are on either side of the normal, so the angle between them is 25° + 25° = 50°.

Which three lie in the same plane at the point of incidence?

A ray hits a curved mirror. Which statement is right?

• The incident ray, the normal and the reflected ray — correct. Yes! That is the second law of reflection.
• The incident ray, the reflected ray and the whole mirror. The mirror surface is not in that plane. It cuts across it at right angles to the normal.
• The two rays only; the normal can lie anywhere. The normal at the point of incidence lies in the same plane too. That is part of the law.
• Curved mirrors follow different laws. In the toy, ∠i = ∠r at every spot of the curved mirrors.
• ∠i = ∠r here too: the normal at that spot is used — correct. Yes! The laws hold for all reflecting surfaces, including spherical ones.
• ∠i = ∠r only at the middle of the mirror. The law holds at every spot. The normal turns from spot to spot, but ∠i = ∠r every time.