Diffraction

Diffraction occurs when waves bend around obstacles or through openings. Single-slit diffraction produces a central bright maximum flanked by weaker side bands. Diffraction gratings are precise tools for spectroscopy.

Key Concepts

Single-slit first minimum: a sinθ = λ
Grating: d sinθ = mλ for principal maxima
Resolving power: R = λ/Δλ = mN
Rayleigh criterion: θ_min = 1.22λ/D
X-ray diffraction: 2d sinθ = mλ (Bragg)

Key Equations

Single-slit dark fringe

a\sin\theta = m\lambda,\quad m=\pm1,\pm2,\ldots

Grating equation

d\sin\theta = m\lambda

Resolving power

R = mN = \frac{\lambda}{\Delta\lambda}

Rayleigh criterion

\theta_{\min} = 1.22\frac{\lambda}{D}

Worked Example

Example Problem

Problem

A diffraction grating has 500 lines/mm and is illuminated by λ=550 nm. Find the angle of the 1st-order maximum.

Solution

d = 1/500 mm = 2×10⁻⁶ m. sinθ = mλ/d = 550×10⁻⁹/2×10⁻⁶ = 0.275. θ = 15.96°.

Practice

Exercises

7 problems

1 of 7

A 600 lines/mm grating is illuminated by λ=500 nm. Find the angle of the m=1 maximum in degrees.

Your answer

degrees

2 of 7

A single slit of width a=0.2 mm is illuminated by λ=600 nm. Find the angular width of the central maximum (2θ₁) in degrees.

Your answer

degrees

3 of 7

A grating has 1200 lines/mm, width 1 cm, illuminated by λ=550 nm. Find the resolving power R in 1st order.

Unlock Exercise 3