Michelson interferometer

The red beam leaves the laser, spreads through a weak negative lens, and splits at the cube. One half goes right to the moving mirror, the other up to the fixed one. Both come back through the cube, and the half of each that turns down lands on the screen.

The screen card shows straight fringes. The moving mirror is turned by 150 microradians, so the two returning beams cross at a small angle and their phase difference changes across the screen.

HeNe laser at 632.8 nm, a −50 mm lens to widen the beam, a 50:50 cube, two flat mirrors 200 mm from the cube and a screen 300 mm below it.

Select the moving mirror and open “Fine adjustment”: the horizontal knob sets the tilt, the piezo moves the mirror along its axis by nanometres.

Two beams of equal power with a phase difference $\Delta\phi$ give an intensity

where $\Delta\ell$ is the difference in optical path. Moving a mirror by $d$ changes the path by $2d$, so one fringe passes for every $\lambda/2$ of travel. Two collimated beams crossing at a small angle $2\theta$, from a mirror turned by $\theta$, make straight fringes with a period $\lambda/2\theta$.

Here the beam spreads from the lens’s focus, so each returning beam seems to come from a point. Turning the mirror moves that point’s image sideways by $2\theta a$, where $a$ is the path from the focus to the mirror, and the fringes are those of two point sources a distance $L$ along the path from the screen:

With $a \approx 470$ mm and $L \approx 970$ mm that is about 4.4 mm, twice the collimated value.

1. Open the screen’s card and count the fringes across a known width to find their period.
2. Change the horizontal knob of the moving mirror and check that the period goes as 1/θ.
3. Move the piezo by 316 nm (half a wavelength) and watch the pattern shift by exactly one fringe.

• Turn table isolation off in the Room tab and watch the fringes dance.
• Turn the laser’s linewidth up to 1 THz, a coherence length of about 0.1 mm: the fringes stay while both arms are equal and fade once the moving mirror is 0.2 mm out.
• Set the horizontal knob to zero so the whole beam is one fringe, put a photodiode where the screen is, and step the piezo: the reading goes from bright to dark and back once per 316 nm of travel, which is how a fringe counter measures distance.