Reflection
Introduced| English | Meaning |
|---|---|
| law of reflection/lɔː ɒv rɪˈflekʃn/ | For reflection at a surface, the angle of incidence equals the angle of reflection, both measured from the normal, and the rays and normal lie in one plane. |
| normal/ˈnɔːml/ | A line perpendicular to a surface at a given point. |
Light bounces off a mirror at a precise angle
- Shine a torch at a mirror and the beam bounces off — but not just anywhere.
- It leaves at exactly the same angle it arrived, mirror-flipped.
- This is the law of reflection 反射定律, obeyed by every mirror and shiny surface.
- Get this one rule and mirror images make perfect sense.
The law of reflection
- Angles are measured from the normal 法线 — the line perpendicular to the surface.
- The angle of incidence equals the angle of reflection: $\theta_i = \theta_r$.
- The incoming ray, the reflected ray and the normal all lie in one plane.
- This holds no matter what the angle — steep or shallow.
A ray strikes a mirror at $30^\circ$ to the normal. At what angle to the normal does it reflect, in degrees?
Difficulty 2/5 · 140 coins + a small bonus on first completion today
$\theta_r = \theta_i = 30^\circ$ by the law of reflection.
The law of reflection states that:
Difficulty 1/5 · 100 coins + a small bonus on first completion today
$\theta_i = \theta_r$, both measured from the normal.
Smooth vs rough surfaces
- A smooth surface (a mirror) reflects a beam neatly — specular reflection.
- A rough surface scatters light every which way — diffuse reflection.
- Both obey $\theta_i = \theta_r$ at each tiny point; the roughness just points the normals every way.
- Diffuse reflection is why you can see this page from any angle.
Why can you read this page from many angles?
Difficulty 1/5 · 100 coins + a small bonus on first completion today
The rough paper scatters light diffusely, so it reaches your eyes from any angle.
Select all true statements about reflection.
Difficulty 2/5 · 140 coins + a small bonus on first completion today
Reflection obeys $\theta_i = \theta_r$ from the normal, smooth = specular. Rough surfaces still obey it at each point.
Always measure from the normal
- The single most common slip is measuring the angle from the surface instead of the normal.
- The normal is the perpendicular line; angles in optics are always taken from it.
- A ray hitting a mirror "flat" ($\theta_i \approx 90^\circ$ from the normal) grazes off almost flat.
- A ray straight down the normal ($\theta_i = 0$) reflects straight back.
The law of reflection
For a mirror, the angle of reflection always equals the angle of incidence - a straight line through the origin.
In optics, angles are always measured from the ____ (the perpendicular line).
Difficulty 1/5 · 100 coins + a small bonus on first completion today
The normal is perpendicular to the surface; all optics angles use it.
A ray at $30^\circ$ to the mirror surface is at $30^\circ$ to the normal.
Difficulty 1/5 · 100 coins + a small bonus on first completion today
False. The surface and the normal are perpendicular, so the angles add to $90^\circ$: the ray is at $60^\circ$ to the normal.
Always measure the angles from the normal (the perpendicular), not from the mirror surface. A ray at $30^\circ$ to the surface is at $60^\circ$ to the normal — and $60^\circ$ is what goes into $\theta_i = \theta_r$.
A ray strikes a mirror at $30^\circ$ to the normal. At what angle does it reflect?
- By the law of reflection, $\theta_r = \theta_i = 30^\circ$ to the normal.
The total angle between the incoming and outgoing rays is $60^\circ$.
The law of reflection: the angle of incidence equals the angle of reflection ($\theta_i = \theta_r$), both measured from the normal. Smooth surfaces give clear specular reflection; rough ones give scattered diffuse reflection. Always measure from the normal.
Write from a reflection angle of 48 degrees
- A ray hits a mirror at 48 degrees to the normal.
- Find the angle of reflection, measured from the normal.
A light ray strikes a plane mirror at 48 degrees to the normal. At what angle to the normal does it reflect, in degrees?
The two angles from the normal are equal, so both are 48 degrees.
At what angle to the normal does the ray reflect?
Difficulty 1/5 · 100 coins + a small bonus on first completion today
Angle of reflection equals angle of incidence. Other options — 30 degrees (the lesson ray); 42 degrees (the angle measured from the mirror surface).