How this calculation works
Two finite-width slits produce closely spaced interference fringes inside a broader diffraction envelope. The envelope and the fringe period come from different dimensions: slit width and slit separation. 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) cos²(πd 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. Adding a second identical slit at 0.5 mm centre spacing creates a paraxial fringe period of 1 mm inside that same envelope.
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
Two finite-width slits produce closely spaced interference fringes inside a broader diffraction envelope. The envelope and the fringe period come from different dimensions: slit width and slit separation.
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 predicts grating orders from a period; this page additionally retains the finite width of each of two slits.
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.
For two slits, spacing means centre-to-centre distance and must be at least the slit width. The plot uses 301 samples and rejects a span too large to resolve the modeled oscillations; reducing the span is preferable to displaying aliased fringes.
Interpret the result
The plotted envelope is sinc squared, multiplied by the two-slit cosine-squared interference factor. At an envelope zero, a geometrical interference maximum can be absent; equal fringe spacing alone does not describe the full intensity pattern.
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.
Adding a second identical slit at 0.5 mm centre spacing creates a paraxial fringe period of 1 mm inside that same envelope.
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 use slit width as well as spacing?
Width sets the diffraction envelope; spacing sets the two-slit interference fringes.
What changes in the comparison?
Increase wavelength and compare the wider envelope and wider fringes.