How this calculation works
A single narrow slit produces a broad central bright region with darker minima on each side. The screen pattern follows interference across the width of that one slit, without requiring a second opening. This page plots normalized far-field intensity as a function of screen position. It also reports the first diffraction minimum and central envelope width so the graph can be checked against explicit geometric quantities.
I/I0 = sinc²(πa sinθ/λ); sinθ = x/√(L²+x²)A worked example
For 500 nm light, a 0.1 mm slit and a screen 1000 mm away, the first minimum is about 5.00006 mm from the centre. The central envelope is therefore about 10.0001 mm wide. Doubling slit width halves the small-angle central width. The change comes from a different range of phase across the opening, not from increasing the screen distance or changing the wavelength.
Good to know
The slits are equally illuminated with coherent monochromatic light at normal incidence. Relative intensity is normalized to one at the central maximum and does not predict optical watts on the detector. Finite coherence, unequal amplitudes, slit-edge imperfections and near-field diffraction are excluded. Before interpreting an experiment, confirm its far-field conditions; a plotted theoretical trace does not establish that the physical setup meets them.
What this calculation answers
A single narrow slit produces a broad central bright region with darker minima on each side. The screen pattern follows interference across the width of that one slit, without requiring a second opening.
This page plots normalized far-field intensity as a function of screen position. It also reports the first diffraction minimum and central envelope width so the graph can be checked against explicit geometric quantities.
The Diffraction grating orders and screen positions calculator uses many equally spaced openings. A single slit instead produces its own continuous diffraction envelope.
Use the right input conventions
Use the width of one slit and the perpendicular distance to a parallel screen. Wavelength is in nanometres; screen coordinates and slit dimensions are in millimetres. The plotted span is measured each side of the centre.
The slit must be wider than one wavelength for a finite first-minimum angle in the supported model. The plot uses 301 samples and rejects a span that would undersample its oscillations rather than drawing a misleading smooth curve.
Interpret the result
The central region extends between the first negative and positive diffraction minima. Its full width is twice the first-minimum screen displacement, not the width of a bright line chosen by eye.
Screen geometry uses the exact relation sinθ = x/√(L²+x²), while any displayed fringe-spacing approximation is explicitly paraxial. The wave model remains Fraunhofer: exact screen mapping does not turn it into a near-field propagation calculation.
Work through the example
For 500 nm light, a 0.1 mm slit and a screen 1000 mm away, the first minimum is about 5.00006 mm from the centre. The central envelope is therefore about 10.0001 mm wide.
Doubling slit width halves the small-angle central width. The change comes from a different range of phase across the opening, not from increasing the screen distance or changing the wavelength.
Where the model stops
The slits are equally illuminated with coherent monochromatic light at normal incidence. Relative intensity is normalized to one at the central maximum and does not predict optical watts on the detector.
Finite coherence, unequal amplitudes, slit-edge imperfections and near-field diffraction are excluded. Before interpreting an experiment, confirm its far-field conditions; a plotted theoretical trace does not establish that the physical setup meets them.
A few questions, answered
Why is the central width twice the first-minimum distance?
The central region runs from the first negative minimum to the first positive minimum.
What changes in the comparison?
Increase wavelength and compare the wider envelope.