Grating interference
About this app
From double slit to grating: raise the number of slits to 1000 and see the principal maxima stay in place and get narrower. Laser, white light and Hg lamp, phasor diagram at the probe, single-slit curve, marks for measuring the spectra. With predictions, exam tasks and a measuring task.
With explain mode: an AI tutor walks you through the app, points out what matters in the scene and answers your questions.
What happens at a grating
Light hits a grating with N slits of spacing g at right angles. In direction α the path difference between neighbouring slits is g · sin α. Principal maxima lie where it is a whole multiple of the wavelength: g · sin α = k · λ. N does not appear in this condition. More slits change neither the position nor the number of the principal maxima. They make the maxima narrower, because N − 1 minima and N − 2 secondary maxima lie between two principal maxima. On the screen, tan α = x/a.
What the app shows
At the top is the intensity curve, below it the glowing screen with a scale in cm, and in front of it fans of light run from the grating to the screen. You can choose a laser, white light or a mercury lamp. The double-slit curve stays for comparison and the single-slit curve shows the envelope. At the probe you see the phasor diagram: in a principal maximum all phasors stand in a line, in a minimum the chain closes. A wave picture shows g and λ in the right ratio. A magnifier, a table of spectra and the resolving power k · N complete the measurement.
What you can try
Drag the number of slits from 2 to 100 and count the principal maxima. Switch to white light and see how the colours blur with three slits and lie apart with many. Set the slit width to b = g/3: the maximum k = 3 is missing. Put two marks on the maxima and compare the small-angle approximation with the exact calculation. There are also six prediction questions, exam tasks with random values and worked solutions, and a measuring task with an unknown laser.
Frequently asked questions
- Why do more slits not give more maxima?
- The position of the principal maxima follows from g · sin α = k · λ, and the number of slits N does not appear there. More slits cancel the light beside the principal maxima more strongly. The principal maxima stay in place and get narrower. The two minima beside a principal maximum are 2λ/(N · g) apart in the sine.
- How do you find the wavelength with a grating?
- You measure the distance x of maximum k from the zeroth maximum and the screen distance a. tan α = x/a gives α, then λ = g · sin α/k. The small-angle approximation λ ≈ g · x/(k · a) gives values that are too large at large angles, about 6 % at α = 20°.
- Why is red on the outside with a grating?
- The angle grows with the wavelength, because sin α = k · λ/g. Red is deflected most and violet least. A prism gives the opposite order. The zeroth maximum stays white because the path difference there is zero for every wavelength.
- How does the app help with exam preparation?
- You put marks on the maxima and see the approximation and the exact calculation side by side. Prediction questions, exam tasks with worked solutions and a measuring task with an unknown laser test your understanding. An explain mode guides you through the scene.
Subject: School physics
More from School physics
- The exposure triangle
- Density and buoyancy
- The Doppler effect
- Additive and subtractive colour mixing
- Franck–Hertz tube (3D)
- Photoelectric effect (3D lab)
- Millikan experiment
- Newton’s cradle and collisions
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