The edge of sharpness

Why does a narrow slit make a wide pattern?

Why does a narrow slit make a wide pattern?

1. Set λ=550 nm and width a=3 µm.
2. Halve the width and compare the first minimum.
3. Increase screen distance without changing the angular pattern.

What to measure

a is slit width; λ is wavelength; β is dimensionless.

The idea underneath

Different parts of an illuminated slit act as coherent contributors. At certain angles their contributions cancel, leaving minima. Narrowing the slit spreads the central maximum; increasing wavelength does the same. This is a far-field intensity model, not a ray shadow. The bench visualises the slit and screen in three dimensions and samples the exact sinc-squared angular pattern.

Build the argument

1. Identify the optical axis and the normal to each interface.
2. Apply reflection, Snell’s law, or the paraxial lens equation according to the model.
3. Check limiting cases: equal indices, object at the focal plane, or a slit much wider than the wavelength.

Worked example 1

λ=500 nm, a=2 µm gives sinθ₁=0.25, θ₁=14.48°.

Worked example 2

At small angles the central width is approximately 2Lλ/a.

Applications

Cameras, microscopes and fibre links combine geometric paths with wave limitations. An image can be sharp geometrically and still be limited by diffraction.

Common misconception

Angles are measured from the normal, not the surface. A virtual image is located by backward ray extensions; no rays physically converge there.

A further investigation

Double slit width and wavelength together. What stays fixed?

Check your understanding

A narrower slit produces…

• A wider central maximum
• A narrower maximum
• No diffraction

Model limits

Monochromatic coherent illumination, single ideal slit, Fraunhofer far field; no near-field diffraction.

OpenStax · Single-slit diffraction