OxfordAQA International AS and A-level Physics: Interference and diffraction: double slits and gratings (9630) – Revision Notes

These notes condense sections 3.5.6 (Interference) and 3.5.7 (Diffraction) of the OxfordAQA International AS and A-level Physics (9630) specification, Version 4.4. Both are shared content for International AS and A-level. For full explanations and derivations, read the study guide, then test yourself with the practice set. Course pages: physics hub and checklist. To find weak spots first, try the free 10-minute diagnostics.

Key definitions

Term	Meaning
Path difference	How much further one wave travels to a point than another
Coherent sources	Same frequency and a constant phase difference
Monochromatic	A single wavelength (a laser is a monochromatic source)
Constructive interference	Waves arrive in phase: path difference nλ
Destructive interference	Waves arrive in antiphase: path difference (n + ½)λ
Diffraction	Spreading of a wave as it passes a gap or an edge
Order n	Whole number labelling a grating maximum (n = 0 is straight ahead)
Grating spacing d	Distance between adjacent slits, d = 1 ÷ lines per metre

Formulas

Quantity	Equation	Notes
Wave speed	v = fλ	Gives λ for sound or microwaves
Fringe spacing	w = λD ÷ s	Small angles, D much greater than s
Grating	d sin θ = nλ	Normal incidence; θ from the straight-through direction
Highest order	n is at most d ÷ λ, rounded down	Since sin θ is never above 1

The relation d sin θ = nλ is derived in the study guide: the path difference between adjacent slits at angle θ is d sin θ, and maxima need this to be nλ.

Young’s double slits in steps

1. Coherent sources: one source, two slits (or a laser through two slits).
2. Each slit diffracts the light, so the beams overlap.
3. Bright fringe where path difference = nλ; dark where (n + ½)λ.
4. Fringes are equally spaced with w = λD ÷ s.
5. Measure across many spacings, then divide by the number of spacings.

Effects on the pattern

Change	Effect on w
Longer wavelength	Increases
Greater slit separation	Decreases
Greater screen distance	Increases
White light instead of laser	Central fringe white, coloured fringes either side, blue inner and red outer

Small worked reminder

A laser of wavelength 500 nm, slits 0.40 mm apart and a screen 2.0 m away give w = 500 × 10⁻⁹ × 2.0 ÷ 0.40 × 10⁻³ = 2.5 × 10⁻³ m = 2.5 mm. Halving s doubles w to 5.0 mm.

Interference with sound and electromagnetic waves

• Sound: two loudspeakers on one signal generator. Loud where path difference is nλ, quiet where it is (n + ½)λ. Example: at 2.0 kHz and 340 m s⁻¹, λ = 0.17 m, so a path difference of 0.34 m (2λ) is loud.
• Microwaves: one transmitter, a metal plate with two slits, a detector moved parallel to the plate. Signal alternates between maxima and minima.
• Radio: two aerials from one transmitter give strong and weak regions.
• Explain with three steps: coherent sources, path difference as a number of wavelengths, in phase or in antiphase.

Required practical 5 and laser safety

• Young’s slits: measure D, measure across ten fringe spacings, calculate λ = ws ÷ D. Plot w against D to use the gradient.
• Grating: measure angles to several orders on both sides of the centre; use d sin θ = nλ.
• Compare percentage uncertainties to see which measurement limits the result.
• Laser safety: low-power laser, never look into the beam or at a shiny reflection, stop the beam at the end of its path with a matt block.

Single-slit diffraction

Light	Pattern
Monochromatic	Bright central maximum, dimmer maxima either side with dark minima between
White	White central maximum; coloured side maxima, blue inner and red outer

Central maximum width (qualitative):

• narrower slit: wider central maximum;
• longer wavelength: wider central maximum;
• wider slit: narrower central maximum.

The intensity against angle graph is not required.

Diffraction gratings

• Many equally spaced slits give sharp, bright maxima at large angles.
• Example: 200 lines per mm gives d = 5.00 × 10⁻⁶ m. For 450 nm, sin θ = 0.090 at n = 1, so θ = 5.16°. The highest order is 5.00 × 10⁻⁶ ÷ 450 × 10⁻⁹ = 11.1, so n = 11 and there are 23 maxima in all.
• White light gives a white n = 0 maximum, then spectra with violet nearest the centre.
• Orders can overlap: with 400 lines per mm, third-order violet (28.7°) falls inside the second-order spectrum (18.7° to 34.1°).
• Uses: measuring wavelengths, identifying elements from line spectra. Spectrometer use is not tested.

Method for grating questions

1. Convert lines per mm to d in metres.
2. Rearrange: sin θ = nλ ÷ d, or λ = d sin θ ÷ n.
3. Check sin θ is not above 1.
4. For the number of maxima, find the highest order n, then count 2n + 1.

Model explanation: bright and dark fringes

Use this order whenever you are asked to explain a fringe pattern.

1. The two slits are lit by the same wavefront, so the sources are coherent.
2. Light diffracts at each slit and the two beams overlap.
3. At a bright fringe the path difference is nλ, so the waves arrive in phase and the displacements add.
4. At a dark fringe the path difference is (n + ½)λ, so the waves arrive in antiphase and the displacements cancel.
5. Equal spacing follows from w = λD ÷ s.

More worked reminders

Microwaves

A transmitter of frequency 10.0 GHz sends waves of speed 3.00 × 10⁸ m s⁻¹ to two slits. Then λ = 3.00 × 10⁸ ÷ 1.00 × 10¹⁰ = 0.0300 m. A detector 0.450 m from one slit and 0.510 m from the other has a path difference of 0.060 m = 2λ, so it records a maximum.

Spacing from a measured fringe pattern

Five bright fringes are spread over 12.0 mm, so there are 4 spacings and w = 3.00 mm. With D = 1.50 m and s = 0.25 mm, λ = ws ÷ D = 3.00 × 10⁻³ × 0.25 × 10⁻³ ÷ 1.50 = 5.0 × 10⁻⁷ m.

Finding the grating spacing

Light of 600 nm gives a second-order maximum at 40.0°. Then d = nλ ÷ sin θ = 2 × 600 × 10⁻⁹ ÷ sin 40.0° = 1.87 × 10⁻⁶ m, which is about 536 lines per mm.

Position on a screen

A grating with d = 4.00 × 10⁻⁶ m and 633 nm light gives sin θ = 0.158 at n = 1, so θ = 9.1°. On a screen 2.00 m away the maximum is 2.00 × tan 9.1° = 0.32 m from the centre. Use tan for the screen distance and sin for the grating equation.

Must-know distinctions

• Interference needs overlapping waves; diffraction is one wave spreading. Both occur in a double-slit pattern.
• Number of fringes is not number of spacings.
• Lines per mm is not d.
• A narrower slit spreads light more; a narrower grating spacing also spreads maxima further apart.

Quick self-test

1. State what makes two sources coherent.
2. Two speakers emit 2.0 kHz sound (speed 340 m s⁻¹). A point is 0.34 m further from one than the other. Is the sound loud or quiet?
3. Calculate w for λ = 500 nm, s = 0.40 mm and D = 2.0 m.
4. Slit separation is halved. What happens to w?
5. A 350 lines per mm grating gives a first-order maximum at 11.0°. Find λ.
6. State the highest order for 700 nm light on a 400 lines per mm grating.
7. Why is the central fringe white in a white-light double-slit pattern?
8. What happens to the central maximum of a single-slit pattern if the slit is made narrower?
9. State two laser safety precautions.
10. Calculate the number of maxima seen with 450 nm light on a 200 lines per mm grating.

Answers

1. Same frequency and a constant phase difference.
2. λ = 0.17 m, so the path difference is 2λ: loud.
3. 2.5 mm.
4. w doubles.
5. d = 2.86 × 10⁻⁶ m, so λ = 2.86 × 10⁻⁶ × sin 11.0° = 5.45 × 10⁻⁷ m (545 nm).
6. d = 2.50 × 10⁻⁶ m; d ÷ λ = 3.57, so the highest order is 3.
7. Path difference is zero for every colour at the centre, so all colours are bright there and add to white.
8. It becomes wider.
9. For example: never look into the beam or its reflection; use a low-power laser; end the beam on a matt block.
10. Highest order 11, so 2 × 11 + 1 = 23 maxima.

Where marks are usually lost

• Using lines per mm as the grating spacing without converting to metres per line.
• Dividing a measured distance by the number of fringes rather than the number of spacings.
• Leaving out the phrase “constant phase difference” when defining coherence.
• Saying fringes “cancel” without stating the path difference as (n + ½)λ.
• Taking the angle from the grating rather than from the straight-through direction.
• Giving a non-whole number for the highest order, or forgetting the maxima on both sides.
• Stating that a wider slit gives a wider central maximum.
• Describing laser safety as “be careful” with no specific precaution.

Official syllabus

OxfordAQA International AS and A-level Physics (9630), sections 3.5.6 and 3.5.7, Version 4.4 (for exams May/June 2020 onwards), published by OxfordAQA.