Mistake Master
Student view — seeing the site as a student does
Home› Unit 13 · Geometric Optics› 13.1·13.2·13.3·13.4
CED objectives

Reflection

▶︎  Watch it animatedinteractive step-through · ~3 min · optional ⚙︎  Open the appletReflection Bench · read one angle from both the normal and the glass, roughen the surface, then block a ray and commit to what the image loses

The law of reflection compares the incident and reflected rays to the normal, the perpendicular to the surface at the strike point, and the two angles are equal. The law holds at every point of every surface: on a rough surface what varies is the direction of the normal from facet to facet, which is why parallel light leaves in many directions and you see the surface rather than an image in it. Every ray a point emits that reaches the optic is redirected to the same image point, so the principal rays drawn in a diagram are a convenient sample of the light rather than all of it.

Three errors dominate. Measuring the angles from the surface instead of from the normal, which reports the complement and agrees with the correct value only at $45^\circ$. Filing diffuse reflection under no-law-applies, which leaves no account of why paper is visible from every seat while a mirror shows the room. And reading a ray diagram as though the object emitted only the two or three rays drawn, so covering half a lens is expected to delete half the image rather than halve its brightness.

the same ray, measured two ways normal 65° 25° from the NORMAL: 65° in, 65° out. This is the law's angle from the SURFACE: 25°, the complement. The two agree only at 45°
Both numbers describe the same ray. Only one of them is the quantity the law of reflection equates.
the law holds at every point; the normals are what differ smooth: one shared normal parallel in, parallel out: you see an IMAGE rough: the normals tilt differently rays fan out: you see THE SURFACE the dashed normals are the only thing that changed between the two panels
Angle in equals angle out on both sides of this figure. Only the dashed normals differ, and that difference is all of diffuse reflection.

The work

3 ways in · any order
Lesson
Reflection ›

Measures every angle from the normal rather than the surface, keeps the law of reflection working facet by facet on a rough surface, and separates where an image forms from how bright it is.

Skill check · 10 scenarios
Open lesson →
Diagnostic
10-item topic check ›

Ten items spanning the failure modes of this topic: measuring the angles from the surface, suspending the law of reflection on a rough surface, and reading a ray diagram as though only the drawn rays exist. Take it cold to find which one is yours, or after the lesson to confirm it is not.

Not started · 10 items · ~15 min
Start diagnostic →
Targeted Practice
Drill a single misconception ›

Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears it for now and moves you to the next. Two in a row is a checkpoint, not proof: if the error resurfaces later, the misconception comes back.

Take the diagnostic to identify your misconceptions
Diagnostic first