Short on time? This page is the recap. For Figures 1 to 3 and the worked examples, use the full study guide.
Recap
- Diffraction: a wave spreads out as it passes through an opening or around the edge of an obstacle. All waves do it.
- Gap-size rule: spreading is strongest when the opening width a is comparable to λ. If a is much larger than λ, the wave passes nearly straight through with a sharp shadow.
- Diffraction does not change v, f or λ. Only the direction of travel spreads.
- Single slit: wavelets from all parts of the slit start in step and interfere on the screen. Result: a wide, bright central band, then dark fringes and dimmer side bands.
- Whether wavelets add or cancel depends on their path length difference. Between the two edges of the slit, ΔL = a sin θ.
- Shape matters: a narrow slit gives stripes; a round hole gives a bright disc with rings. Narrower in a direction means more spreading in that direction.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| ΔL = a sin θ | a = slit width (m); θ from the normal | find the edge-to-edge path difference |
| a sin θ = mλ, m = ±1, ±2, … | λ in m | find the angle of a dark fringe |
| y_min = mλL/a | L = slit-to-screen distance (m); y from the centre (m) | locate dark fringes when θ < about 10° |
| central band width = 2λL/a | side bands are λL/a wide | compare band widths |
| pattern width ∝ λL/a | λ = v/f | predict factor changes |
Assumptions behind the numbers
- The light is monochromatic (one wavelength) and reaches the whole slit in step.
- The screen is far away: L is much larger than a, so rays to one point are nearly parallel.
- y_min = mλL/a needs small angles. Check sin θ = mλ/a; if θ is above about 10°, use tan θ = y/L instead.
- All lengths are in metres before substituting.
Mistakes to avoid
- Calling a sin θ = mλ the bright condition. For one slit it marks the dark fringes.
- Treating m = 0 as dark. The centre is the brightest point.
- Narrower slit, narrower pattern. Wrong way round: the pattern width ∝ 1/a.
- Forgetting the central band is double width. It spans −y₁ to +y₁.
- Changing f but forgetting λ changes. In the same medium, doubling f halves λ and halves the pattern.
- Mixing nm and mm. Convert both to metres.
Quick self-check
- Light of wavelength 500 nm passes through a slit 0.10 mm wide onto a screen 2.0 m away. How far is the first dark fringe from the centre, and how wide is the central band? (10 mm; 20 mm)
- The slit width is doubled and nothing else changes. What happens to the width of the central band? (It halves.)
- At a point on the screen, the edge-to-edge path difference across the slit is 2λ. Is that point bright or dark? (Dark: it is the second-order minimum.)
- Why does sound spread through a doorway much more than light does? (Sound wavelengths are comparable to the doorway width; light wavelengths are about a million times smaller.)
Next: practice questions.