AP® Physics 2: Algebra-Based review sheet from Aim for Five (aimforfive.com/physics-2/units/13/13-1)
Unit 13 · Topic 13.1
13.1 Reflection
Geometric optics models light as rays: straight arrows that show which way the light travels. When a ray bounces off a surface, its angle of reflection equals its angle of incidence, with both angles measured from the normal. Smooth surfaces send reflected light off in one direction (specular reflection), while rough surfaces scatter it every which way (diffuse reflection). Since 2024–25, mirrors and lenses have their own unit; older materials pair them with interference and diffraction, which are now in Unit 14.
Key terms
- light ray
- ray diagram
- normal line
- law of reflection
- specular reflection
- diffuse reflection
Light as a ray
A light wave spreads out as wavefronts, like ripples on a pond. A ray is a straight arrow drawn perpendicular to those wavefronts, pointing the way the wave moves. In this unit you'll ignore the wave nature of light and just follow rays.
The ray model works when the objects light meets (mirrors, lenses, windows) are much bigger than light's wavelength, which is only about 400 to 700 nanometers for visible light. It fails when light squeezes through tiny openings. Then light spreads out and interferes, and you need the wave model from Unit 14.
A laser is the cleanest example of a ray in real life: a narrow beam of a single color that you can aim and trace across a lab bench.
A ray diagram is a sketch that shows the path of light before and after it hits something. Draw rays with a ruler, put arrowheads on them to show direction, and draw the surfaces and normals carefully. Most optics questions start with one.
The normal and the law of reflection
The normal is an imaginary line drawn perpendicular (at 90°) to a surface at the point where a ray hits it. Draw it as a dashed line. Every angle in optics is measured from the normal, not from the surface.
The angle of incidence is the angle between the incoming ray and the normal. The angle of reflection is the angle between the outgoing ray and the normal. The law of reflection says they're equal: .
Two more details matter. The incoming ray, the reflected ray and the normal all lie in the same flat plane. And the reflected ray ends up on the opposite side of the normal from the incoming ray, like a ball bouncing off a wall.
If a problem gives you the angle between the ray and the surface, subtract it from 90° first. A ray that skims in at 20° to a mirror has an angle of incidence of 70°.
Specular and diffuse reflection
The law of reflection holds at every point on every surface. What changes is the direction of the normal.
On a smooth surface like a mirror or still water, the normal points the same way everywhere a beam lands. Parallel incoming rays leave as parallel reflected rays. That's specular reflection, and it's why you can see a clear image in a mirror.
On a rough surface like paper, a wall or a T-shirt, the surface is bumpy on a tiny scale, so the normal points in a different direction at each spot. Parallel incoming rays leave in many different directions. That's diffuse reflection. It's why you can see a sheet of paper from anywhere in the room, but you can't see your face in it.
So diffuse reflection doesn't break the law of reflection. Each ray still obeys relative to its own local normal.
Reflection from more than one mirror
When a ray hits two or more mirrors, handle one bounce at a time. Draw the normal at each point of contact, apply there, then follow the reflected ray to the next surface. Geometry, mostly the fact that the angles in a triangle add to 180°, links one bounce to the next.
A useful result: if you rotate a mirror by an angle α while the incoming ray stays fixed, the reflected ray turns by 2α. The angle of incidence changes by α, and so does the angle of reflection, so the total angle between the two rays changes by 2α.
Worked examples
Try each one yourself first, then open the solution.
- Example 1
Angle from the surface (classic trap)
A laser beam strikes a flat mirror, making an angle of 25° with the mirror's surface. What is the angle of reflection, and what is the angle between the incoming and reflected beams?
Show the solutionHide the solution
- Step 1: Angles are measured from the normal, which is perpendicular to the mirror. The angle of incidence is 90° − 25° = 65°.
- Step 2: By the law of reflection, the angle of reflection is also 65°.
- Step 3: The incoming and reflected beams are on opposite sides of the normal, so the angle between them is 65° + 65° = 130°. (Check: the reflected beam also makes 25° with the surface, and 180° − 25° − 25° = 130°.)
- Step 4: The trap is answering 25°, which is the angle with the surface, not with the normal.
Answer: Angle of reflection 65°; the beams are 130° apart.
- Example 2
Two mirrors at a right angle
Two flat mirrors meet at a 90° corner. A ray hits the first mirror with an angle of incidence of 30°, reflects, and then hits the second mirror. Find the angle of incidence at the second mirror and the direction of the final ray compared with the original ray.
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- Step 1: After the first bounce, the ray leaves at 30° from the first mirror's normal, which means it makes 90° − 30° = 60° with the first mirror's surface.
- Step 2: The ray, the first mirror and the second mirror form a triangle. The corner angle is 90° and the angle at the first mirror is 60°, so the angle between the ray and the second mirror's surface is 180° − 90° − 60° = 30°.
- Step 3: The angle of incidence at the second mirror is measured from its normal: 90° − 30° = 60°. It reflects at 60°.
- Step 4: The two angles of incidence add to 30° + 60° = 90°. Each bounce reverses one component of the ray's direction (first the component perpendicular to mirror 1, then the component perpendicular to mirror 2), so both components end up reversed. The final ray travels parallel to the original ray but in the opposite direction.
Answer: Angle of incidence 60° at the second mirror; the ray goes back the way it came, on a parallel path.
- Example 3
Rotating a mirror
A laser beam hits a flat mirror at an angle of incidence of 20°. The mirror is rotated 10° so that the angle of incidence becomes 30°. By how much does the direction of the reflected beam change?
Show the solutionHide the solution
- Step 1: Before: the angle between the incoming and reflected beams is 2 × 20° = 40°.
- Step 2: After: the angle between them is 2 × 30° = 60°.
- Step 3: The incoming beam didn't move, so the reflected beam swung through 60° − 40° = 20°, twice the mirror's rotation.
Answer: The reflected beam turns 20°.
Common mistakes
- Measuring angles from the surface instead of the normal. Draw the normal first, every time, and measure from it.
- Thinking diffuse reflection breaks the law of reflection. Every ray still obeys it; the normals just point in different directions on a rough surface.
- Drawing the reflected ray on the same side of the normal as the incoming ray. It belongs on the opposite side.
- Using the ray model to explain light spreading through a narrow slit. Spreading and interference need the wave model (Unit 14).
On the exam
- Expect to draw or complete ray diagrams. Points come from a drawn normal, equal angles marked on both sides of it, and arrowheads showing the direction of travel.
- Questions often ask why you can see an object from many angles, or why a wet road shows glare. Answer in terms of smooth versus rough surfaces and the direction of the normal.
Connected topics
Videos
Check yourself
4 questions on 13.1 Reflection. Pick an answer to see if you got it, and why.
A narrow beam of light strikes a flat mirror. The beam makes an angle of 35° with the surface of the mirror. What is the angle of reflection?
A ray of light reflects from a plane mirror. The angle between the incident ray and the reflected ray is 80°. What is the angle of incidence?
A laser beam hits a plane mirror. The beam stays fixed while the mirror is rotated by 12° about an axis in its surface, perpendicular to the plane containing the beam and the normal. Through what angle does the reflected beam turn?
Several students sitting in different parts of a room can all read the same paper poster on the wall, but none of them can see their own reflection in it. Which explanation is best?
0 of 4 answered