Diffraction
Diffraction is wave spreading produced by an opening or obstacle, and it becomes most pronounced when the opening size is comparable to the wavelength. A single slit produces a broad central maximum and dark minima whose positions depend on slit width, wavelength, and screen distance.
Diffraction: quick answer
Diffraction is wave spreading produced by an opening or obstacle, and it becomes most pronounced when the opening size is comparable to the wavelength. A single slit produces a broad central maximum and dark minima whose positions depend on slit width, wavelength, and screen distance. A single slit is not just a narrow geometric ray bundle. Every part of the opening contributes to the outgoing wave, so destructive interference produces dark minima and the central maximum widens as the aperture becomes small relative to wavelength.
Use the single-opening diffraction model here. Use the small-angle screen-position approximation only for θ<10°; otherwise use the angular relation directly.
What you should be able to explain and do
Use these as closed-note retrieval prompts before opening the worked reasoning.
Explain why diffraction becomes stronger as aperture size approaches wavelength.
Use a sinθ=mλ to locate single-slit minima.
Use small-angle geometry to connect angular minima with screen positions when appropriate.
Predict how λ, a, and L change the central maximum width.
Key terms for this wave model
Definitions stay next to the model so no important term requires leaving the lesson to understand the explanation.
diffraction
diffraction is wave spreading associated with passage through an opening or around an obstacle.
aperture
aperture is an opening through which a wave passes.
single-slit pattern
single-slit pattern is a broad central bright region with weaker side maxima separated by minima.
diffraction minimum
diffraction minimum is a direction or screen position where destructive interference from different parts of the slit produces low intensity.
far-field pattern
far-field pattern is a diffraction pattern observed sufficiently far from the aperture for angular relationships to be useful.
small-angle approximation
small-angle approximation is the approximation sinθ≈tanθ≈θ for sufficiently small θ in radians.
Match every relationship to its conditions
Some Unit 14 relationships are intentionally qualitative. Keep the variable meanings, geometry, and scope attached to each statement.
| Relationship / model | Variables & units / meaning | When to use it | Physical anchor |
|---|---|---|---|
a sinθ_m = mλ | a slit width (m); θ_m dark-minimum angle; m=1,2,…; λ wavelength (m) | single-slit diffraction minima | a narrower slit makes the first minimum occur at a larger angle |
y_m ≈ mλL/a | y_m dark-minimum position from center (m); λ wavelength (m); L screen distance (m); a slit width (m) | single-slit small-angle geometry | increasing screen distance spreads the observed pattern |
central maximum width ≈ 2λL/a | central width (m); λ wavelength (m); L screen distance (m); a slit width (m) | estimating the distance between the first minima on opposite sides at small angle | doubling λ approximately doubles the central-maximum width |
What the diagram or graph must show
Translate physical situation ↔ diagram/graph ↔ relationship ↔ verbal prediction.
Aperture sketch
compare a≫λ and a≈λ to visualize spreading.
Angular pattern
central maximum centered at θ=0 with first minima on both sides.
Screen pattern
mark central width as the distance between the first minima.
Trend table
λ↑ or L↑ widens; a↑ narrows.
Change one wave condition and inspect what responds
Predict first, then move one control. The tool is constrained to the topic model rather than introducing extra equations.
Two examples with model selection exposed
Each example identifies the representation/condition before the arithmetic or qualitative conclusion.
First minimum
Situation: λ=600 nm light passes through a=0.20 mm slit.
Reasoning: sinθ₁=λ/a=(6.0×10⁻⁷)/(2.0×10⁻⁴)=0.0030.
θ₁≈0.0030 rad≈0.17°.
Screen width
Situation: The same pattern is observed at L=2.0 m.
Reasoning: First minimum y≈λL/a=0.0060 m; central width is twice that.
Central maximum width ≈0.012 m=1.2 cm.
Recognize the physics before reaching for an equation
Use the cue to choose the model, connect it to nearby ideas, then reject any method whose assumptions do not match the situation.
What should trigger Topic 14.7?
Use diffraction when a wave passes an opening or obstacle comparable to its wavelength and spreads into the geometric-shadow region.
How this idea fits the course
Diffraction is a direct wave-model limit on geometric optics and becomes quantitatively connected to interference patterns in 14.8.
Scope check before solving
Use the single-opening diffraction model here. Use the small-angle screen-position approximation only for θ<10°; otherwise use the angular relation directly.
Turn the model into measurable evidence
Plan what changes, what is measured, which representation tests the model, and what uncertainty would weaken the conclusion.
Investigation target
Project monochromatic light through several slit widths, measure first-minimum positions and central widths, and test the predicted λL/a scaling with uncertainty.
Reasoning errors to eliminate
Repair the representation or scope decision before doing more arithmetic.
Six things to do before moving on
Use these as closed-note transfer prompts.
- I can identify the relevant wave representation before choosing an equation.
- I can define every wavelength, frequency, period, angle, aperture/slit spacing, index, or film thickness I use.
- I can predict the qualitative trend before calculating a numerical result.
- I can state when a relationship is qualitative-only or relies on a small-angle/normal-incidence assumption.
- I can translate between physical pattern, diagram/graph, equation/model statement, and verbal claim.
- I can design or critique a wave experiment and justify a conclusion from data and uncertainty.
Practice is kept on its dedicated pages
Finish the lesson first. Then open the separate topic bank when you want exam-style practice without replacing the teaching content above.
42 multiple-choice questions
Use the exact-topic MCQ bank to test model selection, representations, calculations and boundaries after learning the concept.
Open 42 Topic MCQs4 multipart free-response tasks
Use the exact-topic FRQ set for mathematical, representation, experimental and qualitative/quantitative reasoning.
Open 4 Topic FRQsTopic 14.7 FAQs
When is diffraction most noticeable?
When the opening/obstacle size is comparable to wavelength.
What determines the first minimum?
a sinθ₁=λ.
What happens if wavelength increases?
The pattern spreads more.
What happens if slit width decreases?
The central maximum becomes wider.
Why is the central maximum broad?
It extends between the first minima on opposite sides.