Explore optical diffraction

What you will learn

• Distinguish wavelength from slit width.
• Interpret the single-slit intensity equation.
• Use a model to explore parameter dependence.

The concept

For an ideal single slit under Fraunhofer conditions, normalized intensity is I/I₀ = (sin β / β)², where β = πa sin(θ)/λ. Here a is slit width, λ is wavelength and θ is the observation angle.

The first minima occur when a sin(θ) = ±λ. At small angles, the screen displacement is approximately proportional to λL/a, where L is the screen distance. This is an approximation; near-field diffraction requires a different model.

Worked example

Calculate and plot the normalized single-slit diffraction intensity.

lambda = 550e-9; % wavelength (m)
a = 50e-6;       % slit width (m)
L = 1;            % screen distance (m)
x = linspace(-0.015, 0.015, 1000);
theta = atan(x/L);
beta = pi*a*sin(theta)/lambda;
I = ones(size(beta));
idx = abs(beta) > 1e-12;
I(idx) = (sin(beta(idx))./beta(idx)).^2;
plot(x*1e3, I, 'LineWidth', 2);
xlabel('Screen position (mm)'); ylabel('I / I_0'); grid on;

The model uses a small-angle-compatible screen geometry and the far-field single-slit expression. Real systems may include finite source size, detector response, aberrations and alignment errors.

Try it yourself

Predict the effect of changing the aperture.

Where this is used

Diffraction models support optical system design, aperture analysis, imaging, spectroscopy and understanding resolution limits.