Reflection and Mirrors

The video lesson for this topic is coming soon.

Essential Question

Why do you see yourself in a mirror?

You look in a mirror every day, but where is the person you see? By the end of this lesson, you should be able to use the law of reflection, tell specular and diffuse reflection apart, and draw a ray diagram that locates the image in a plane mirror.

The Law of Reflection

Angle in = angle out
θ_i = θ_r
Both measured from the normal

A ray diagram. A horizontal mirror is at the bottom. A dashed vertical line, the normal, rises from the point where the light hits. The incident ray comes in from the upper left and the reflected ray leaves to the upper right. The angle between each ray and the normal is marked: theta i on the left and theta r on the right, and they are equal.

When light bounces off a surface, the angle of incidence (θ_i, the incoming ray) equals the angle of reflection (θ_r, the outgoing ray). Both angles are measured from the normal, an imaginary line perpendicular to the surface at the point where the light hits. This rule is called the law of reflection.

The Normal Line

Line at 90° to the surface
Draw it dashed
Measure from it, not the mirror

A ray hits a horizontal mirror. A dashed normal line stands straight up from the hit point with a small square showing a 90 degree angle. The angle between the ray and the normal is marked in green as 30 degrees. The angle between the ray and the mirror surface is marked in red as 60 degrees. Caption: measure from the normal, not the mirror.

The normal is an imaginary line drawn perpendicular (at 90°) to a surface at the point where a ray hits it. We draw it as a dashed line because it isn’t a real ray of light. In this picture, the ray makes a 30° angle with the normal and a 60° angle with the mirror’s surface. The angle of incidence is the 30° angle. Always measure from the normal.

Specular vs. Diffuse Reflection

Smooth surface: rays stay parallel
Rough surface: rays scatter
Mirror vs. paper

Top: three parallel rays hit a smooth surface and reflect as three parallel rays, labeled specular, smooth. Bottom: three parallel rays hit a jagged rough surface and reflect in three different directions, labeled diffuse, rough.

On a smooth surface like a mirror or still water, parallel rays reflect as parallel rays. This is specular reflection, and it makes a clear image. On a rough surface like paper or a wall, each tiny bump faces a different way, so parallel rays scatter in all directions. This is diffuse reflection. Every ray still obeys the law of reflection, but the normals point in different directions. Diffuse reflection is why you can see a piece of paper from anywhere in the room, but you can’t see your reflection in it.

Images in a Plane Mirror

Image appears behind the mirror
Same size, same distance
Virtual: no light really goes there

A vertical mirror in the middle. On the left, a solid red upright arrow labeled object. On the right, behind the mirror, a dashed red upright arrow of the same height labeled image. Double arrows below show both are the same distance d from the mirror.

A flat mirror is called a plane mirror. The image it makes appears to be behind the mirror. It is the same size as the object, upright, and the same distance behind the mirror as the object is in front. It is a virtual image: light rays only seem to come from it. No light actually travels behind the mirror, so you could never project this image onto a screen.

Ray Diagram: Plane Mirror

Rays leave the object
Reflect: θ_i = θ_r
Extend reflected rays back, dashed
They meet at the image

A ray diagram with a vertical mirror. Two rays leave the top and bottom of an upright object arrow, hit the mirror, and reflect into an eye on the left. At each hit point there is a short dashed normal line. Dashed lines extend the reflected rays back behind the mirror, where they meet at the top and bottom of a dashed image arrow.

To find the image, draw rays from the object to the mirror. At each point where a ray hits, draw a dashed normal and reflect the ray so the angle of reflection equals the angle of incidence. The reflected rays spread apart and enter the eye. Your brain assumes light travels in straight lines, so it traces those rays straight back. Extend the reflected rays behind the mirror as dashed lines: they meet at the image. Since the rays don’t really go there, the image is virtual.

Worked Examples

Try each problem on your own first, then check your work against the solution.

Example 1: Angle of Reflection

A light ray strikes a plane mirror at an angle of 35° from the normal. What is the angle of reflection?

A ray hits a horizontal mirror, making a 35 degree angle with the dashed normal. The reflected ray is drawn with a question mark for its angle.

Knowns: θ_i = 35°, measured from the normal
Law of reflection: θ_r = θ_i
Substitute: θ_r = 35°
Answer: θ_r = 35° from the normal, on the other side of the normal

Example 2: Angle from the Surface

A ray of light makes a 25° angle with the surface of a mirror. Find the angle of incidence and the angle of reflection.

A ray hits a horizontal mirror at a shallow angle. The angle between the ray and the mirror surface is marked 25 degrees. A dashed normal stands at the hit point.

Knowns: the ray makes 25° with the mirror surface
Convert: the normal is 90° from the surface, so θ_i = 90° − 25°
Angle of incidence: θ_i = 65°
Angle of reflection: θ_r = θ_i, so θ_r = 65°

Common mistake: answering 25°. That angle is measured from the surface, not the normal.

Example 3: Angle Between Rays

A ray hits a mirror with an angle of incidence of 28°. What is the angle between the incident ray and the reflected ray?

Knowns: θ_i = 28°
Law of reflection: θ_r = θ_i = 28°
Add the angles: the normal sits between the two rays, so the angle between them is θ_i + θ_r = 28° + 28°
Answer: 56°

Example 4: Image Distance

You stand 1.5 m in front of a plane mirror. How far are you from your image?

A stick figure stands 1.5 m in front of a vertical mirror. Behind the mirror, a dashed gray stick figure shows the image.

Knowns: object distance = 1.5 m in front of the mirror
Plane mirror rule: image distance = object distance = 1.5 m behind the mirror
Add: distance from you to your image = 1.5 m + 1.5 m
Answer: 3.0 m

Big Ideas

θ_i = θ_r, measured from the normal
Smooth: specular. Rough: diffuse
Plane mirror image: same size, same distance
Image is virtual, behind the mirror

Back to the essential question: light reflects off a smooth mirror with the angle of reflection equal to the angle of incidence, both measured from the normal. When you trace the reflected rays back, they seem to come from a point behind the mirror, so you see a virtual image of yourself, the same size and the same distance behind the mirror as you are in front. Next up, we’ll see what happens when light goes into a new material instead of bouncing off in Refraction.