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17.3Interference and Diffraction

Diffraction Gratings and Applications — American System Physics Revision Notes & Topical Questions

5 min read 7 parts Lesson 5 of 5 1 quiz

📚 American System Physics Hub / Topical Revision
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Lesson summary

Describe the diffraction grating and the pattern it produces.Grating equationgrating spacing × sine of angle = order × wavelength, d sin θ = mλ (d and λ in m).Grating spacingd = 1/N, where N = lines per metre (e.g.

  • Maximum order
  • Angle from screen measurements
  • Spectroscopy
  • Grating spacing (d)
  • Spectrometer
  • Emission line spectrum

Section 1 of 7Diffraction Gratings and Applications

Essential knowledge
17.3 Diffraction Gratings and Applications concept map: Grating equation, Grating spacing, Maximum order, Angle from screen measurements, Spectroscopy
Visual guide to the key ideas explained in this lesson.
A grating works like many slits at once. Light from every slit interferes; only at angles where the path difference between neighbouring slits is a whole number of wavelengths do all the waves reinforce, giving very sharp, bright maxima.
The path difference between neighbouring slits at angle θ is d sin θ, which gives the condition d sin θ = mλ.
A finer grating (more lines per mm, smaller d) produces larger angles and fewer orders.
With white light, each order (except zero) becomes a spectrum with violet nearest the centre and red farthest out; higher-order spectra may overlap.
Gratings give much sharper, brighter maxima than a double slit, so wavelengths can be measured to high precision.
Spectroscopy
Spectroscopy light from a gas discharge tube or a star is passed through a grating. The line positions reveal the elements present; for stars, shifts in line positions reveal motion (redshift).
The closely spaced tracks on a CD or DVD act as a reflection grating, producing rainbow colours.
Holograms, security images on bank cards and anti-reflective lens coatings all use interference and diffraction of light.
Polarizing filters show that light is a transverse wave; together with interference and diffraction this supports the wave model of light.
Always convert lines per mm to lines per m before calculating d: multiply by 1000.

Section 2 of 7Process & sequence

1
Mount a grating of known lines per mm at right angles to a laser beam; place a screen a measured distance D away, parallel to the grating.
2
Mark the zero-order spot and the first-order spots on each side on the screen.
3
Measure the distance y from the zero order to each first-order spot and average the two sides.
4
Calculate the angle: tan θ = y/D, then find θ.
5
Calculate the grating spacing d = 1/(lines per metre).
6
Use λ = d sin θ/m; repeat with second-order spots and compare.

Measuring λ with a gratingwrite these steps in this order; each step is a marking point.

1
Convert lines per mm into lines per metre, N.
2
Find grating spacing d = 1/N.
3
Measure the angle θ of an order m (or find it from tan θ = y/D).
4
Apply λ = d sin θ / m.
5
Check that m ≤ d/λ and quote λ to sensible significant figures.

Section 3 of 7Compare

Double slit versus diffraction grating
FeatureDouble slitGrating
Number of slits2Hundreds to thousands per mm
MaximaBroad, many, evenly spacedVery sharp, bright, few
AnglesSmallLarge (easily measured)
Equationλ = xd/Ld sin θ = mλ
Precision of λModerateHigh

Section 4 of 7Worked examples

A grating has 300 lines per mm. Laser light gives first-order maxima at 11.0° from the centre. Find the wavelength.
  • N = 300 × 1000 = 3.00 × 105 m−1;
    • d = 1/N = 3.33 × 10−6 m. λ = d sin θ/m = 3.33 × 10−6 × sin 11.0° / 1 = 3.33 × 10−6 × 0.191 = 6.36 × 10−7 m (636 nm).
36.9°
Light of wavelength 500 nm falls on a grating with 600 lines per mm. (a) Find the angle of the second order. (b) Find the highest order visible.
  • d = 1/(6.00 × 105) = 1.67 × 10−6 m.
    • (a) sin θ2λ/d = 2 × 5.00 × 10−7/1.67 × 10−6 = 0.600, θ = 36.9°.
    • (b) d/λ = 1.67 × 10−6/5.00 × 10−7 = 3.33, so highest order m = 3.
A first-order spot is 0.26 m from the centre on a screen 1.20 m from a grating with d = 2.5 × 10−6 m. Find λ.
  • tan θ = 0.26/1.20 = 0.217, θ = 12.2°. λ = d sin θ = 2.5 × 10−6 × 0.211 = 5.3 × 10−7 m.

Section 5 of 7Key terms

Section 6 of 7Command terms

Command terms
Identify / Describe (FRQ)
A short, specific statement; describing requires relevant characteristics, not a single word.
Explain / Justify (FRQ)
Give the cause-and-effect reasoning or evidence; a restated fact does not score.
Calculate
Show setup, substitution and the answer with units.
Predict
State the expected outcome; add a reason only if asked to justify.
MCQ technique
Read every option; eliminate distractors that are true statements but do not answer the question; watch for NOT/EXCEPT.

Section 7 of 7Exam technique

Keywords the mark scheme looks for in this lesson

Keywords the mark scheme looks for in this lesson
Diffraction grating · Grating spacing (d) · Order (m) · Grating equation · Spectrometer · Emission line spectrum · Continuous spectrum · Maximum order · Holography · Iridescence · Polarization
Learn each definition in the Key words tab exactly; a missing keyword in a definition usually loses the mark.

How to get full marks (examiner guidance)

1
Answer exactly what is asked; extra correct material does not earn credit, and contradictory statements can cancel credit (AP FRQ).
2
Use precise vocabulary, never “it/stuff/things”.
3
Show units and working in calculations.
4
In MCQs, predict the answer before reading the options, then eliminate.

Words to avoid

1
d = number of lines per mmd = 1/N, where N is the number of lines per metre.
2
sin θ can be greater than 1 for higher ordersan order exists only if mλ/d ≤ 1.
3
the grating refracts light into coloursthe grating diffracts light and the waves from the slits interfere.
4
violet is deviated most by a gratingred (longest λ) is deviated most by a grating.
5
use tan θ = mλ/duse sin θ = mλ/d; tan θ is only for finding θ from screen distances.

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