Law of Reflection — Angle of Incidence Equals Angle of Reflection
The law of reflection: angle of incidence equals angle of reflection. Learn specular vs diffuse reflection, how mirrors form images, and real uses.
Quick answer
The law of reflection says a light ray bounces off a surface so that its angle of incidence equals its angle of reflection — both measured from the normal. Smooth surfaces give sharp mirror images; rough surfaces scatter light diffusely.
Unit: Angles in degrees
Example: Shine a laser at a mirror at 30° to the normal and it leaves at 30° on the other side — like a billiard ball bouncing off a cushion at equal angles.
What you will learn
- State the law of reflection with angles measured from the normal
- Distinguish specular from diffuse reflection
- Locate the virtual image in a plane mirror
- Explain why rough surfaces show no mirror image
- Apply the law to periscopes and retroreflectors
One rule for every bounce
Throw a ball at a wall and it bounces back symmetrically. Light does the same — with perfect mathematical precision. The law of reflection governs every mirror, every glint of sunlight on water, and every periscope ever built.
Draw an imaginary line perpendicular to the surface at the bounce point — the normal. The incoming ray makes an angle of incidence () with the normal; the outgoing ray makes an angle of reflection (). The law:
Mirrors vs walls: order vs chaos
Why does a mirror show your face while a wall shows only itself? Both reflect light — the difference is order.
- Specular reflection (mirror): the surface is smooth on the scale of light's wavelength (~500 nm). Parallel incoming rays stay parallel after bouncing, preserving the image.
- Diffuse reflection (wall, paper): microscopic roughness scatters rays in all directions. The light still bounces — you see the wall because of it — but the image information is scrambled.
Even the best mirror is not perfect; even dull paper reflects. It is a spectrum, not a switch.
Where your mirror image really is
Stand before a plane mirror. Light from your face hits the mirror and reflects into your eyes. Your brain assumes light travels straight, so it traces those rays backward to a point behind the mirror — where your image appears to stand.
No light actually exists behind the glass, so the image is virtual: upright, same size, and exactly as far behind the mirror as you are in front. This is also why ambulance lettering is written backward — in your rear-view mirror it reads correctly.
Hold a finger near a mirror and slowly move it toward the glass. Your image's finger approaches at the same speed — image distance always equals object distance.
Two mirrors are better than one
Two reflections solve problems one cannot:
- Periscopes use two parallel mirrors at 45° to shift your line of sight over walls or above water.
- Corner reflectors (three mutually perpendicular mirrors) send any incoming ray exactly back where it came from — the trick behind bicycle reflectors, road signs, and the mirror arrays astronauts left on the Moon for laser ranging.
- Kaleidoscopes multiply one view into symmetric patterns with angled mirrors.
Each bounce obeys . Chain enough bounces and light goes wherever geometry commands.
Variables and units
| Symbol | Name | Unit | Meaning |
|---|---|---|---|
| Angle of incidence | degrees | Angle between incoming ray and the normal | |
| Angle of reflection | degrees | Angle between reflected ray and the normal |
Common mistakes
Mirrors actually reverse front and back — the axis perpendicular to the surface. Your left hand appears on the left side of the image; it looks like your right hand only because you mentally rotate yourself to face the image.
Both angles are measured from the normal (perpendicular to the surface), not from the surface itself. Measuring from the surface gives the complement and wrong predictions.
They reflect plenty — diffusely. A white wall reflects most incident light, just scattered in all directions. That scattered light is exactly how you see the wall.
Real-world applications
Mirrors: bathroom mirrors, car rear-view mirrors, and telescope mirrors all rely on the law of reflection to form faithful images.
Periscopes: submarines and tanks use two angled mirrors to see over obstacles — each bounce obeys θi = θr.
Solar concentrators: curved mirror arrays focus sunlight onto a single point to generate steam for power plants.
Road safety: retroreflectors on signs and bicycles bounce headlight beams straight back to drivers using multiple reflections.
Frequently asked questions
What is the law of reflection?
The angle of incidence equals the angle of reflection (θi = θr), both measured from the normal — the imaginary line perpendicular to the surface at the point of contact. This single rule predicts every mirror image.
Why can I see myself in a mirror but not in a wall?
A smooth surface (mirror) reflects rays in parallel — specular reflection — giving a clear image. A rough surface (paper, wall) scatters rays in all directions — diffuse reflection — so you see the surface itself but no mirror image.
Is a mirror image real?
No. The image is virtual — it appears to be behind the mirror where no light actually goes. Your brain traces the diverging reflected rays backward to a point behind the glass. That is why you cannot project a mirror image onto a screen.
Where exactly is my mirror image?
The image is the same distance behind the mirror as you are in front, the same size, upright, and laterally inverted (left-right swapped). Move 1 m closer and your image moves 1 m closer too.