Physics · Wave optics
Single slit diffraction calculator.
Enter the slit width, the wavelength and the screen distance. Get the angles of the dark fringes and the width of the bright central band.
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Single slit diffraction
Light passing through a narrow slit of width a produces a pattern with dark fringes (minima) at a sinθ = mλ for m = ±1, ±2, ±3 and so on. The wide bright band between the first two minima is the central maximum, and its angular half-width is the first minimum, sinθ1 = λ/a. A narrower slit makes the pattern wider.
Worked example. 633 nm light through a 10 µm slit: λ/a = 0.0633, so the first minimum is at θ = 3.63°. On a screen 2 m away the minimum is 2 × tan(3.63°) = 0.127 m from the centre, so the central bright band is 0.254 m (25.4 cm) wide. If the slit is narrower than the wavelength, sinθ would exceed 1 and there are no dark fringes at all.
Frequently asked questions
What is the single slit diffraction formula?
Dark fringes occur at a sin(theta) = m lambda, for m = 1, 2, 3 (on either side), where a is the slit width.
How wide is the central maximum?
Between the two first minima. On a screen at distance L it is 2 L tan(theta1), where sin(theta1) = lambda / a. For a small angle that is about 2 lambda L / a.
Why does a narrower slit give a wider pattern?
The first minimum sits at sin(theta) = lambda / a, so reducing the slit width a increases the angle.
What if the slit is smaller than the wavelength?
Then lambda / a is above 1 and no minimum exists. The light spreads over a very wide angle.
Is the same equation used for double slits?
No. A double slit adds interference bright fringes at d sin(theta) = m lambda inside this single-slit envelope.
Sources
Checked
- OpenStax University Physics Vol. 3: Key equations, ch. 4 (single-slit minima a sin theta = m lambda)
- OpenStax University Physics Vol. 3, sec. 4.1: Single-Slit Diffraction
OpenStax gives the minima condition. Screen positions y = L tan(theta) and the central width are geometry applied to that formula. Runs entirely in your browser. Nothing you type is sent or stored.
Scope
Far-field (Fraunhofer) classroom model for a slit much longer than it is wide.