Practice a College Board-style free response question on Waves, Sound, & Physical Optics. Write your response, then reveal the model answer to see exactly what earns each point.
Free Response Question · Unit 6 · Double-Slit Interference
Monochromatic light of wavelength 600 nm (6.0 × 10⁻⁷ m) passes through two narrow slits separated by a distance of 0.20 mm (2.0 × 10⁻⁴ m). The resulting interference pattern is observed on a screen.
Quantity
Value
Wavelength, λ
6.0 × 10⁻⁷ m
Slit separation, d
2.0 × 10⁻⁴ m
A
Explain, in terms of path length difference, the condition required to produce a bright fringe at a given point on the screen.
✓ Model answer (earns the point)
A bright fringe occurs at a point where the path length difference between the light traveling from the two slits to that point equals a whole number of wavelengths: path difference = mλ, where m = 0, ±1, ±2, .... At this condition, the two waves arrive at the screen exactly in phase (crest aligning with crest), producing constructive interference and a bright fringe.
Why it scores: States the mathematical condition (mλ) explicitly, AND explains the physical reasoning (waves arriving in phase → constructive interference) rather than just naming the formula.
B
If the slit separation were decreased while keeping the wavelength and screen distance constant, predict what would happen to the spacing between adjacent bright fringes on the screen. Justify your answer.
✓ Model answer (earns the point)
The fringe spacing would increase. Decreasing the slit separation d means a smaller distance between the slits produces the same path-length difference (mλ) only at a LARGER angle (and corresponding larger position) on the screen. Since slit separation and fringe spacing are inversely related, a smaller d results in WIDER spacing between adjacent bright fringes.
Why it scores: Correctly predicts the direction of change (fringe spacing increases), AND justifies it with the inverse relationship between slit separation and fringe spacing, rather than just stating the answer without reasoning.
C
Explain why this interference pattern would NOT be observed if the two slits were illuminated by two separate, ordinary (incoherent) light bulbs instead of a single coherent light source split between the two slits.
✓ Model answer (earns the point)
A stable interference pattern requires the light from the two slits to maintain a constant phase relationship over time (coherence). Two separate ordinary light bulbs emit light with rapidly and randomly fluctuating phases relative to each other, since they are independent sources with no fixed relationship. As a result, the locations of constructive and destructive interference would shift randomly and rapidly — far faster than the eye (or any detector) could track — averaging out into a uniform, featureless illumination rather than a stable fringe pattern.
Why it scores: Identifies coherence (constant phase relationship) as the missing requirement, explains why independent light bulbs lack this property, AND connects the loss of coherence to the practical outcome (washed-out, non-distinct pattern) rather than just stating "they're not coherent."
How to score points on AP Physics 2 FRQs
State the bright/dark fringe condition explicitly (mλ or (m+½)λ) before reasoning about it. Graders want to see the relevant relationship, not just a conclusion.
Connect "in phase" and "out of phase" language to constructive/destructive interference explicitly. Don't just say "they interfere" — say HOW (in phase → constructive → bright).
For "predict and justify" prompts, state the direction of change AND the reasoning, in that order. A direction without justification, or justification without a clear answer, both lose points.
When asked to explain failure of a setup (like incoherent sources), name the specific missing physical requirement (coherence) and describe its consequence. Vague answers like "it just wouldn't work" earn little credit.
Keep your explanations grounded in wave behavior — phase, path difference, superposition — rather than vague statements about light "mixing."