Reflection
Distinguish rays from wavefronts and apply reflection angles to the local normal.
AP Physics 2 Topic 13.1 · College Board CED printed p. 94, 95 / PDF p. 101, 102 · See this topic in the course outline
Start by asking what your line means. A ray shows where light travels; a wavefront shows equal phase. Once the ray reaches a surface, draw its normal before measuring any angle.
Before you start
- Perpendicular lines and complementary angles
A ray is perpendicular to a wavefront
A quick wave bridge: phase means the position within a repeating cycle, such as crest versus trough. A wavefront joins points at the same phase. Frequency is the number of cycles per second, measured in hertz (Hz); wavelength is the distance between neighboring equal-phase fronts, such as successive crests. Coherent waves keep a stable phase relationship, and monochromatic means approximately one frequency. These terms describe the usual laser beam; detailed interference calculations wait until Unit 14.
A light ray is an arrowed straight line indicating the direction light travels in a uniform medium. It is perpendicular to a light wave’s wavefront, a surface of equal phase. For parallel wavefronts, draw parallel rays at right angles to the fronts; for circular wavefronts expanding from a point in a uniform medium, draw outward radial rays. The wavefront is not the path traveled by the light.
Geometric optics works when dimensions such as mirror sizes and apertures are much larger than the wavelength, so wave spreading can be neglected for the question. A laser provides a coherent, approximately monochromatic beam that can often be represented by a ray or a narrow bundle of rays. That representation does not mean lasers lack wave behavior. Interference and diffraction require the wave model of Unit 14; a ray alone cannot explain light spreading behind a small opening or an interference pattern.
A ray diagram traces the incoming path, the interaction point, and the outgoing path, with arrows indicating travel. Continue a straight path through a uniform medium and change its direction only where the physical interaction calls for it. A dashed extension is a geometric construction, not a light path.
Measure reflection angles from the normal
Light incident on a surface can be reflected. At the point of incidence draw the normal, a line perpendicular to that surface. The incident ray points toward the surface and the reflected ray away; both lie on the incident-medium side. The law of reflection is , with both angles measured between the ray and the normal. An angle of 25° to the surface is 65° to the normal. Never substitute one angle convention into a formula written for the other.
Rough and smooth surfaces obey the same local law
Specular reflection occurs when the illuminated surface is smooth enough that its local normals are approximately parallel. Parallel incoming rays then leave in a common direction. Diffuse reflection occurs from a rough surface whose local normals vary, sending parallel incoming rays into different reflected directions. Each tiny patch still obeys θᵢ = θᵣ relative to its own normal. Diffuse reflection does not mean that the reflection law fails.
This explains why matte paper is visible from many directions, while a flat polished mirror directs a narrow reflected bundle toward only certain viewing positions. A curved smooth surface can also have varying normals across it: “smooth” refers to local roughness, not necessarily a globally flat shape.
Turn wavefronts into rays
A diagram has three horizontal wavefronts advancing upward in air. A student draws light rays along the horizontal fronts. Repair the diagram and explain when that ray picture could fail.
Draw vertical arrows upward, perpendicular to each horizontal front.
Why this step? The ray represents propagation direction; the front represents equal phase.
If the beam goes through an opening comparable to its wavelength, spreading requires a wave model rather than straight rays alone.
Why this step? The geometric approximation has a size-based limit.
Answer and check
Upward vertical rays. A small-opening diffraction pattern needs the Unit 14 wave description.
Convert a surface angle before reflection
A beam strikes a flat mirror at 32° to the mirror surface. Find the incidence and reflection angles to the normal, and describe the outgoing path.
Draw the normal perpendicular to the surface. θᵢ = 90° − 32° = 58°.
Why this step? The stated angle and incidence angle are complementary.
θᵣ = θᵢ = 58°. The reflected ray is on the same side of the mirror as the incoming ray and leaves at 32° to the surface.
Why this step? Apply the reflection law with the same normal-angle convention on both sides.
Answer and check
Incidence 58° and reflection 58° to the normal; outgoing path 32° to the surface.
Try it from memory
Write your answer and reason before opening the worked answer. Your self-assessment is a study decision; it is not an automatically graded score.
Question 1
Circular wavefronts expand from a point source in a uniform medium. What direction should the rays have?
Worked answer and reason
Radially outward, perpendicular to the circular fronts.
The normal to a circular front is radial, and the arrow follows travel.
Question 2
Can the fact that a laser beam is narrow prove that it cannot diffract? Explain.
Worked answer and reason
No. A coherent, approximately monochromatic laser beam can be modeled as a ray for suitable geometry, but it still exhibits wave diffraction and interference.
A model choice does not remove the underlying wave nature.
Question 3
A reflected ray makes 20° to a flat surface. What was its incidence angle?
Worked answer and reason
70° to the normal.
Convert to the normal angle before applying θᵢ = θᵣ.
Question 4
A rough surface sends parallel rays in different directions. Does that violate reflection?
Worked answer and reason
No. The normals differ from patch to patch, so equal local incident/reflected angles can yield different outgoing directions.
The law is local; it uses the normal at each incidence point.
JavaScript enables saved drafts and self-assessment. You can always work on paper.
Catch the tempting mistake
- A ray lies along a wavefront.
- A ray is perpendicular to a wavefront and points in the propagation direction.
- Reflection angles are measured from the mirror surface.
- The law uses the normal, perpendicular to the local surface.
- Diffuse reflection breaks the reflection law.
- Every local patch obeys the law; its normal differs from neighboring patches.
Put it to work
Give the physical reason as well as the calculation. The worked solutions are on a separate page.
- Problem 1 · wavefront-to-ray translation
- Problem 2 · ray sketch and comparison
- Problem 9 · experimental design and graph
- Problem 10 · comparison table and ray translation
Scientific calculator workspace
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Scientific calculator
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For the teacher
- Draw arrows on incident and reflected rays; missing arrows can hide a reversed path.
- Use a mirror and matte paper to compare reflected directions at the same incident angle.
- Discuss laser ray models alongside a slit demonstration, while leaving interference calculations to Unit 14.
Source objectives and scope
Suggested skills are teaching guidance. The course applies all science practices across its objectives.
Science references for this teaching
- College Board AP Physics 2 CED, Unit 13 (supplied pinned source) — Official Unit 13 requirements, plane/spherical mirror scope, and magnitude form of magnification
- OpenStax College Physics 2e: The Ray Aspect of Light — Ray and wavefront geometry; geometric-optics approximation
- OpenStax College Physics 2e: The Law of Reflection — Normal-angle law and local diffuse/specular reflection
- OpenStax College Physics 2e: Image Formation by Mirrors — Paraxial spherical mirrors, mirror distances, magnification
- OpenStax College Physics 2e: The Law of Refraction — Refractive index, speed, and Snell angles
- OpenStax College Physics 2e: Total Internal Reflection — Index-order condition and critical-angle boundary
- OpenStax College Physics 2e: Image Formation by Lenses — Thin-lens images, sign convention, and principal rays
Glossary and deeper reading · 6 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Wavefront
A wavefront is a surface joining points of equal wave phase at a given time. Rays are perpendicular to wavefronts in the uniform isotropic ray model used here. For example, a distant source can be approximated by nearly plane wavefronts over a small region.
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Oscillation phase
Phase specifies the position within a repeating oscillation cycle. A phase difference tells how much one oscillation leads or lags another at a chosen place and time. For example, two sinusoidal waves half a cycle out of phase can cancel when their amplitudes are equal.
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Wave
A wave is a propagating disturbance that can transfer energy without transporting the medium as a whole. Mechanical waves require a material medium, while electromagnetic waves can propagate through vacuum. For example, a pulse travels along a rope while individual rope segments move locally around their equilibrium positions.
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Frequency
Frequency is the number of complete repeating cycles per unit time. It is measured in hertz, meaning cycles per second, and is the reciprocal of the period. For example, a vibrating string with a higher frequency produces more cycles each second.
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Wavelength
Wavelength is the spatial distance between neighboring points at the same phase of a periodic wave. It connects propagation speed and frequency through speed equal to frequency times wavelength. For example, neighboring crests of a sinusoidal water wave are separated by one wavelength.
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Coherence
Coherence describes a sufficiently stable phase relationship between waves for a sustained interference pattern. It depends on the sources and on the time or distance over which their phase relationship remains predictable. For example, illuminating two slits with one suitable monochromatic source produces a stable relative phase at the slits.