Width of the single-slit central maximum
The central maximum runs from the first minimum on one side to the first minimum on the other, so its angular width is 2λ/b and its width on a screen a distance D away is approximately 2λD/b. It is twice as wide as each secondary maximum and much brighter.
half-width: sin θ₁ = λ/b · full width on screen ≈ 2λD/bWhat this actually means
The factor of two is the whole trap. sin θ = λ/b gives one edge only. Doubling is needed for the full width, and it is the most common lost mark in this section.
Worked pattern: λ = 580 nm, b = 0.310 mm, D = 2.00 m gives sin θ₁ = 1.87 × 10⁻³, so the half-width on the screen is 3.74 mm and the full central maximum is about 7.5 mm across.
The secondary maxima are only λD/b wide because they sit between consecutive minima that are λD/b apart. That is why the central peak stands out so clearly.
Everything scales inversely with b. A narrower slit gives a wider and dimmer central maximum, because less light gets through and it is spread over a larger area.
With white light the central maximum stays white in the middle but its edges show colour, because the red minima lie further out than the violet ones.
Quoting λD/b as the width of the central maximum when that is only its half-width.
Prove it — watch it be true
- In the single-slit view, mark the first minimum either side of the centre.
- Confirm the measured span between them is twice the λD/b half-width.
- Compare that span with the spacing of the next pair of minima and confirm the central peak is twice as wide.