How to use it
A Michelson interferometer splits one beam of light in two, sends the halves along two arms to two mirrors and brings them back together on a screen. Where the waves arrive in step the screen is bright; where they arrive half a wavelength apart it is dark. One fringe corresponds to a mirror movement of half a wavelength, about 0.3 µm for red light, so the instrument measures tiny distances, or a wavelength when the distance is known.
Start with the red laser and drag sideways across the screen: rings grow out of the centre or shrink into it. Then run the motor and watch the counter, and finally try the exercise, where you find a hidden wavelength by counting fringes yourself.
Controls
- Screen and diagram: drag sideways to move mirror M2 (100 px = 1 µm).
- Keyboard on the screen: left and right arrows move the mirror 10 nm, Shift with an arrow 1 µm, Page Up and Page Down 10 µm; Space starts or stops the motor, Escape stops it, C counts a fringe, Z zeroes the counter.
- Motor: 0.05 to 10 µm/s in either direction; the label shows the fringes per second.
- +1, −1 and Zero counter: your own count, next to the automatic count of the detector at the mark.
- Sliders: coarse position from −1000 to +1000 µm in 1 µm steps plus a fine adjust of ±5 µm in 0.01 µm steps, or type d.
- Sources: lasers at 632.8 nm, 532 nm or any wavelength from 380 to 750 nm, a sodium lamp and white light.
How it works
Light going to the movable mirror crosses the extra distance twice, so a mirror shift d makes a path difference Δ = 2d. For one wavelength λ and two equal beams the brightness is
Light reaching the screen at an angle θ to the axis has a path difference of about 2d cos θ, so the bright fringes are rings with 2d cos θ = mλ. The page treats the spread-out beam as two point sources, the images of the source in the two mirrors, and computes the path difference to every point of a screen 0.5 m away and 100 mm across. As |d| grows, new rings appear in the centre and the pattern gets denser; near d = 0 the whole screen brightens and darkens together.
Each time the mirror moves λ/2, one fringe passes the mark:
Counting 20 fringes over 6.33 µm gives 633 nm. The detector counts up and down, like a real fringe counter with two detectors.
Tilting the fixed mirror by α turns its beam by 2α. Near zero path difference the rings then become nearly straight fringes, about λ/(2α) apart where the beams leave the mirrors and wider on the screen because the beam keeps spreading.
A sodium lamp emits two lines, 589.0 and 589.6 nm. Their patterns drift in and out of step, so the contrast fades and returns every λ²/(2Δλ) ≈ 0.29 mm of mirror travel; the 589.0 nm line is about twice as strong, so the contrast drops to one third rather than zero. With white light the patterns of all wavelengths agree only near Δ = 0: a few coloured fringes there, an even white field elsewhere. The page adds up a flat spectrum in 5 nm steps with the CIE 1931 colour matching functions. In this ideal model zero path difference is bright; a real beam splitter can add a half-wave shift that makes it dark.
The 30 mm gas cell adds 2L(n − 1), and n − 1 grows in proportion to pressure (about 2.7 × 10−4 for air at 20 °C and normal pressure). Pumping it out moves fringes past the mark: n − 1 = Nλ/(2L).
Things to try
- Zero the counter, run the motor at +0.2 µm/s with the red laser and stop after 30 fringes. The mirror should have moved about 9.49 µm.
- Choose white light, set d to 0 and tilt the mirror a little. Move 2 µm away and the colours are gone.
- With the sodium lamp, set the chart range to 2 mm and measure the spacing of the low-contrast zones to get Δλ.
- Turn on the gas cell, press Pump out and count the fringes for air, helium and carbon dioxide.
- Do the exercise counting 10 fringes, then 40, and compare your errors.
Frequently asked questions
Why rings and not one bright spot?
Different parts of the screen receive light at slightly different angles, and the path difference depends on the angle. Points at the same angle form circles around the axis.
Why are white-light fringes so hard to find?
White light stays coherent over only about a micrometre, so the two arms must be equal to within roughly that.
What are interferometers used for today?
Measuring lengths with laser wavelengths, testing the flatness of lenses and mirrors, spectroscopy, and detecting gravitational waves with arms several kilometres long.
Who invented it?
Albert A. Michelson built the first one in 1881. In 1887 he and Edward Morley looked with it for the Earth’s motion through the supposed ether and found none; in 1907 he received the Nobel Prize in Physics.
Sources
- Michelson AA (1881). The relative motion of the Earth and of the luminiferous ether. American Journal of Science s3-22(128), 120–129. Michelson’s first interferometer and his 1881 search for the ether.
- Michelson AA, Morley EW (1887). On the relative motion of the Earth and the luminiferous ether. American Journal of Science s3-34(203), 333–345. The 1887 experiment that found no ether drift.
- Ciddor PE (1996). Refractive index of air: new equations for the visible and near infrared. Applied Optics 35(9), 1566–1573. Its equations give n − 1 ≈ 2.7 × 10−4 for air at 20 °C and normal pressure.