Short on time? This page is the recap. For Figures 1 to 3 and the worked examples, use the full study guide.
Recap
- A double-slit pattern needs diffraction (each slit spreads the light so the beams overlap) and interference (the overlapping waves add).
- The same wavefront reaches both slits, so the two waves start in step. The path difference to a point on the screen is d sin θ.
- Whole number of wavelengths: bright. Odd number of half-wavelengths: dark.
- Interference alone gives evenly spaced, equally bright fringes. Real slits have width, so the fringes sit inside the single-slit envelope; a fringe where the envelope is zero is missing.
- Young’s experiment: dark fringes mean light from two slits can cancel, which particles cannot do. This is evidence that light behaves as a wave.
- Grating: many evenly spaced slits. Same angles as two slits, but the maxima are much sharper and brighter.
- White light on a grating: central maximum white; each order is a spectrum with violet nearest the centre and red farthest.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| ΔL = d sin θ | d = slit separation (m) | find the path difference |
| d sin θ = mλ, m = 0, ±1, … | λ in m | locate bright fringes or grating maxima |
| d sin θ = (m + ½)λ | m = 0, 1, 2, … each side | locate double-slit dark fringes |
| y_max = mλL/d; spacing λL/d | L = slit-to-screen distance (m) | small angles only (θ < about 10°) |
| d = 1/N | N = lines per metre (convert from lines/mm) | find d for a grating |
| highest order: largest m < d/λ | sin θ < 1 for a visible order | count visible orders |
Assumptions behind the numbers
- Monochromatic light (unless the question says white light), reaching all slits in step.
- The screen is far away: L much larger than d.
- y_max = mλL/d needs small angles. Grating angles are usually large: use tan θ = y/L.
Mistakes to avoid
- Swapping the single- and double-slit rules. With d: bright. With a: dark.
- Bigger d, wider fringes. Wrong way round: spacing ∝ 1/d.
- Leaving lines/mm unconverted. 400 lines/mm gives d = 2.5 × 10⁻⁶ m.
- Small-angle form for a grating.
- Violet farthest out. In a grating, red is farthest; the prism order is the reverse.
- Counting a missing fringe. Check where the envelope is zero.
Quick self-check
- λ = 600 nm, d = 0.30 mm, L = 2.0 m. What is the fringe spacing? (4.0 mm)
- What is the path difference at the second dark fringe from the centre? (1.5λ)
- A grating has 500 lines/mm. For 450 nm light, find the first-order angle and the highest order. (13.0°; m = 4, since d/λ = 4.44)
- Why is the central maximum white for white light? (At θ = 0 every wavelength has zero path difference.)
Next: practice questions.