To construct a reflected ray, draw the normal at the point where the ray hits the mirror, measure the angle of incidence from the normal, then draw the reflected ray at the same angle on the other side of the normal. This law, angle of incidence = angle of reflection, holds for every flat reflecting surface.
This skill opens light and imaging and returns in refraction, periscopes, optical fibres and every image diagram that follows.
What is the normal, and why does everything depend on it?
The normal is an imaginary line drawn at 90° to the surface at the point where the ray strikes. It is drawn dashed so it is not confused with a ray. All angles in optics are measured from the normal, never from the surface.
The angle of incidence, i, is between the incident ray and the normal. The angle of reflection, r, is between the reflected ray and the normal. The law of reflection says i = r, and the incident ray, the normal and the reflected ray all lie in the same plane.
How do I construct the reflected ray, step by step?
- Draw the mirror as a straight line with shading or hatching on the back.
- Mark the point of incidence where the incident ray meets the mirror.
- Draw the normal at 90° to the mirror at that point, dashed, using a protractor or set square.
- Find the angle of incidence between the incident ray and the normal. If the question gives the angle to the mirror, subtract it from 90°.
- Mark the same angle on the other side of the normal and draw the reflected ray with a ruler.
- Add arrows to show the direction of both rays, and label i and r.
Worked example
A ray of light makes an angle of 35° with a flat mirror. (Invented example data.) Draw the reflected ray and state the angle between the incident and reflected rays.
Step 1, draw the normal: at the point of incidence, at 90° to the mirror.
Step 2, find i: the ray is 35° from the mirror, so it is 90° − 35° = 55° from the normal. i = 55°.
Step 3, apply the law: r = i = 55°. The reflected ray leaves 55° from the normal on the far side, which is also 35° from the mirror.
Step 4, find the angle between the rays: 55° + 55° = 110°.
Step 5, check: the reflected ray must be on the opposite side of the normal from the incident ray, and the angle between the ray and the mirror is 35° on both sides. Both hold, so the diagram is consistent.
How does a plane mirror form an image?
The image in a plane mirror is as far behind the mirror as the object is in front of it. The line joining an object point to its image point meets the mirror at 90°.
The image is virtual (the rays only appear to come from it), the same way up as the object, the same size as the object, and laterally inverted. A person standing 1.5 m in front of a plane mirror sees their image 1.5 m behind it, so the distance from person to image is 3.0 m.
The mistake to watch for
A very common slip is to measure the angle of incidence from the mirror surface instead of the normal.
Mistaken answer: “The ray is 35° from the mirror, so the reflected ray is 35° from the normal.”
The 35° was measured from the surface, but the law of reflection uses angles from the normal.
The correction is to convert first. The angle to the normal is 90° − 35° = 55°, so the reflected ray is 55° from the normal. A quick check is that the reflected ray must make the same angle with the mirror as the incident ray does, here 35° on each side.
Check yourself
Try these, then open each answer.
1. A ray hits a plane mirror with an angle of incidence of 40°. What is the angle between the incident ray and the reflected ray?
Show answer
The angle of reflection is also 40°, so the angle between the two rays is 40° + 40° = 80°.
2. A ray makes an angle of 20° with the surface of a plane mirror. What is the angle of reflection?
Show answer
Angle of incidence = 90° − 20° = 70°. The angle of reflection equals it, so it is 70°.
3. A student stands 2.4 m in front of a plane mirror and then walks 0.5 m toward it. How far is the student from their image now?
Show answer
The new distance to the mirror is 2.4 − 0.5 = 1.9 m. The image is 1.9 m behind the mirror, so the distance from student to image is 1.9 + 1.9 = 3.8 m.
Where this leads next
With the normal habit secure, move on to using a refraction relationship, where the same measuring rule applies to light bending at a boundary. When you reach images, the plane mirror is the simplest example of a virtual image in real and virtual image construction.
Some students can state the law of reflection but still draw the angle from the wrong line under exam pressure. That is the kind of habit our teachers look for in online one-to-one Physics tuition.