Geometric Optics

Four topics on where light goes and where the image ends up. Reflection, with every angle measured from the normal and the law holding on a rough surface as well as a smooth one, images in mirrors and what a negative distance reports, refraction, where a change of speed bends the ray and can trap it entirely, and images in lenses, including the case inside the focal length that a magnifying glass runs on.

AP exam 12-15%4 topics

Topics

13.1

Reflection

Images Formed by Mirrors

Refraction

Images Formed by Lenses

Lesson

Diagnostic

after diagnostic

Key forms For every problem in this unit

Every angle in this unit

measured from the NORMAL, the perpendicular to the surface at the strike point. Never from the surface

Law of reflection

θ(incident) = θ(reflected). Holds at EVERY point of every surface, rough or smooth

Diffuse reflection

the law still holds; what varies is the direction of the normal from facet to facet

Index of refraction

n = c/v, so n ≥ 1. Higher n means SLOWER light in that medium

Snell's law

n₁ sinθ₁ = n₂ sinθ₂. Each index multiplies the angle in its OWN medium

Which way it bends

into a SLOWER medium (higher n): TOWARD the normal, smaller angle. Into a faster one: away. Along the normal: straight through

What changes at a boundary

speed and wavelength both divide by n. FREQUENCY does not change: the source set it

Wavelength in a medium

λ = λ₀/n, with f fixed and v = fλ

Critical angle

sinθ(c) = n₂/n₁, and ONLY when the light starts in the higher-index medium. A sine above 1 means no critical angle exists

Total internal reflection

past θ(c), nothing is transmitted. High index to low only

Dispersion

n depends slightly on wavelength: violet sees a larger n in glass, so it slows more and bends more. A property of the MATERIAL, so a vacuum shows none

Mirror and thin-lens equation

1/s(i) + 1/s(o) = 1/f. A sum of RECIPROCALS: invert only at the last step

Magnification (CED form)

|M| = |h(i)/h(o)| = |s(i)/s(o)|. The magnitude is the size ratio

Its sign, as this course writes it

M = h(i)/h(o): NEGATIVE means inverted, positive means upright. Size and orientation are separate readings

Focal length signs

CONVERGING (concave mirror, convex lens): f > 0. DIVERGING (convex mirror, concave lens): f < 0

Spherical mirror

f = R/2, inheriting the sign

Reading s(i)

positive = real, on the side the light actually goes. NEGATIVE = virtual, on the other side. A result, not an error

Real vs virtual

real: rays physically cross, a screen catches it. Virtual: rays only appear to come from there. BOTH are visible to a placed eye

Plane mirror

image as far behind as the object is in front; virtual, upright, same size. Object-to-image separation is TWICE your distance

Diverging optic, any object

always upright, reduced, virtual. That fixed outcome is the check on the arithmetic

Converging optic, object inside f

upright, enlarged, VIRTUAL. This is the magnifying glass, and it is a legitimate case

Principal rays

all three start at the TIP of the object and bend once, at the line through the optic's centre. Not at the glass faces, not at a focal point

Unit 13 tools

Challenge bank

1 / 60

60 open-ended problems.

Read the question, work it out, then flip the card to compare your reasoning to the worked solution. Mark each card so you can return to the ones that still bite.

Question

Tap card to reveal explanation

Worked solution

Tap card to return to question

Cumulative assessment

Test the unit.

Twenty mixed items drawn from across all 4 topics, with guaranteed misconception-code coverage. Identifies which misconceptions still bite when you cannot see which topic the question came from.

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Check what stuck.

Units 9 through 13, drawn evenly so earlier units get the same share as this one. Twenty questions or a full 42-question section, your choice. Even coverage means this is a retention check rather than a score estimate.

20 or 42questions

29topics

108codes covered

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