Law of reflection

When light meets a surface and reflects, the direction in which it leaves is related to the direction from which it arrived. The arriving light is represented by the incident ray, and the light leaving the surface is represented by the reflected ray.

To describe their directions, draw an imaginary line perpendicular to the surface at the point where the incident ray meets it. This line is called the normal.

The angle of incidence, $$i$$, is the angle between the incident ray and the normal. The angle of reflection, $$r$$, is the angle between the reflected ray and the normal. Both angles are measured from the normal, not from the surface.

The law of reflection states that these two angles are equal:

For example, if an incident ray makes an angle of $$30^\circ$$ with the normal, the reflected ray leaves on the other side of the normal at $$30^\circ$$ to it. The same law works in reverse: if the direction of the reflected ray is known, its angle to the normal gives the angle of incidence.

Plane-mirror image formation

Light from an object reflects at a plane mirror and reaches an observer’s eyes. The observer sees the reflected light as if it had travelled in straight lines from a point behind the mirror.

If the reflected rays from a point on the object are extended backwards, their extensions meet at the corresponding image point behind the mirror. Light does not actually pass through that point, so the image is virtual.

The image is the same size as the object. It is also the same distance behind the mirror as the object is in front of it. These distances are measured perpendicular to the mirror.

Plane-mirror ray constructions

A ray diagram shows the path of light using straight lines with arrowheads. An incident ray travels towards the mirror; a reflected ray travels away from it. A ruler keeps the lines straight, and a protractor is used to measure angles.

Constructing a reflected ray

1. Draw the plane mirror as a straight line and draw an incident ray meeting it. Add an arrowhead pointing towards the mirror.
2. At the point where the ray meets the mirror, draw the normal: a line perpendicular to the mirror surface.
3. Measure the angle of incidence between the incident ray and the normal.
4. On the other side of the normal, draw the reflected ray at the same angle. Add an arrowhead pointing away from the mirror.

The angle between the reflected ray and the normal is the angle of reflection. If $$i$$ is the angle of incidence and $$r$$ is the angle of reflection, the construction follows:

Both angles are measured from the normal, not from the mirror surface.

Locating the virtual image

To locate the image of a point on an object, draw two rays from that point to different points on the mirror. Construct the reflected ray for each incident ray, using a normal at each point where a ray meets the mirror.

Use dashed lines to extend the reflected rays backwards behind the mirror. The extensions meet at the apparent image point. This is a virtual image: the reflected light travels away from the mirror, but appears to come from the point behind it.

Measure the object’s distance from the mirror along a line perpendicular to the surface. The image is the same perpendicular distance behind the mirror as the object is in front:

For example, if an object point is $$4\ \text{cm}$$ in front of the mirror, its image point is $$4\ \text{cm}$$ behind it.

Angles from the mirror surface

The normal is at $$90^\circ$$ to the mirror, so an angle measured between a ray and the mirror surface is complementary to the corresponding angle measured from the normal: the two add to $$90^\circ$$.

For example, if an incident ray makes $$30^\circ$$ with the mirror surface, its angle of incidence is $$90^\circ - 30^\circ = 60^\circ$$. The angle of reflection is therefore also $$60^\circ$$ from the normal.