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Flashcards · AP® Physics 2: Algebra-Based · Unit 13

Unit 13: Geometric Optics flashcards

26 cards on topics 13.1 to 13.4. Pick a topic or study the whole unit.

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13.1 Reflection

What is the law of reflection?
θᵢ = θᵣ, with both angles measured from the normal. The incident ray, normal and reflected ray lie in one plane, with the rays on opposite sides of the normal.
A ray makes 20° with a mirror surface. What is the angle of reflection?
70°. Convert first: angle from the normal = 90° − angle from the surface. Measuring from the surface is the most common error.
A mirror turns through 6° while the incident ray stays fixed. How far does the reflected ray turn?
12°. Turning a mirror by φ turns the reflected ray by 2φ.
What is the difference between specular and diffuse reflection?
Specular: a smooth surface, normals all the same, parallel rays stay parallel and a clear image forms. Diffuse: a rough surface, normals vary patch to patch, rays scatter. Every patch still obeys the law.
What is a light ray, and when does the ray model work?
A straight line at 90° to the wavefronts, pointing the way the wave travels. It works when the wave nature of light can be ignored; it cannot explain diffraction or interference.
What must a ray diagram include?
Ruled straight rays with arrows showing direction, and a dashed normal at each point of reflection. Light paths are reversible.

13.2 Images Formed by Mirrors

Where is the focal point of a concave and a convex mirror?
Concave: rays parallel to the axis reflect through F, in front of the mirror. Convex: they reflect as if from F behind the mirror. f ≈ R/2; a plane mirror's F is infinitely far away.
What is the mirror equation, with its sign conventions?
1/sᵢ + 1/sₒ = 1/f, distances from the vertex. f is positive for concave, negative for convex. sᵢ positive: real image in front; negative: virtual image behind.
What is the difference between a real and a virtual image?
Real: reflected rays actually meet, so the image can be caught on a screen. Virtual: rays only appear to meet (behind a mirror); draw those extensions as dashed lines.
An object is 30 cm from a concave mirror with f = 10 cm. Describe the image.
1/sᵢ = 1/10 − 1/30 = 2/30, so sᵢ = 15 cm in front. Real, inverted, |M| = 15/30 = 0.50, reduced.
What image does a convex mirror always form?
Virtual, upright and reduced, between the vertex and F behind the mirror, wherever the object is.
What are the principal rays for a mirror?
Parallel ray: reflects through (or from) F. Vertex ray: reflects symmetrically about the axis. Focal ray: through (or towards) F, reflects parallel.
How do you describe an image fully?
State its location, type (real or virtual), orientation (upright or inverted) and size (|M| = |hᵢ/hₒ| = |sᵢ/sₒ|: enlarged, reduced or same size).

13.3 Refraction

Why does light refract?
Its speed changes at the boundary between media; the frequency does not change. A ray along the normal slows down but does not bend.
What is the index of refraction?
n = c/v, with c = 3.00 × 10⁸ m/s and no units. Higher n means lower speed. Light at 2.40 × 10⁸ m/s in a plastic gives n = 1.25.
What is Snell's law?
n₁ sin θ₁ = n₂ sin θ₂, with angles from the normal and each n paired with the angle in its own medium. Into a higher n the ray bends towards the normal; into a lower n, away.
When does total internal reflection happen?
Only going into a lower n, at an angle beyond the critical angle: sin θc = n₂/n₁. At exactly θc the refracted ray runs along the surface. Glass (1.52) to air gives θc ≈ 41.1°.
A ray in air meets water (n = 1.33) at 45°. What is the angle of refraction?
sin θ₂ = sin 45° / 1.33 ≈ 0.532, so θ₂ ≈ 32.1°, towards the normal. Check the calculator is in degrees.
How do you find n from refraction data?
Plot sin θ_air against sin θ_material (not the angles themselves). The straight line's slope is n.

13.4 Images Formed by Lenses

How do converging and diverging lenses differ?
Converging (thicker in the middle): parallel rays meet at F on the far side; f positive. Diverging (thinner in the middle): parallel rays spread as if from F on the incident side; f negative.
What is the thin lens equation?
1/sᵢ + 1/sₒ = 1/f, distances from the lens midline. Rearranged: 1/sᵢ = 1/f − 1/sₒ; take the reciprocal at the end. sᵢ positive: real; negative: virtual.
A converging lens has f = 20 cm and the object is 25 cm away. Where is the image?
1/sᵢ = 1/20 − 1/25 = 1/100, so sᵢ = +100 cm. Real, inverted, |M| = 100/25 = 4.0.
How does the image of a converging lens change with object distance?
Beyond 2f: real, inverted, reduced. At 2f: same size. Between f and 2f: real, inverted, enlarged. At f: no image. Inside f: virtual, upright, enlarged (a magnifying glass).
What image does a diverging lens form?
Always virtual, upright and reduced, for any real object.
What happens to the image if half a lens is covered?
The full image still forms, but dimmer, because fewer rays reach each image point.
How do you find a lens's focal length from data?
Plot 1/sᵢ against 1/sₒ. The line has slope −1 and both intercepts equal 1/f.

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