The Michelson Interferometer · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Counting fringes to measure tiny shifts

Science · Waves, Light & Sound · ages 20-22
Name ______________________   Date ____________

  1. M1 moves exactly half a wavelength. How many fringes pass your mark?

    • None, the pattern freezes
    • Two, one per arm
    • One

  2. In the Michelson layout, what does the half-silvered mirror do?

    • Merges two lasers into one beam
    • Splits one beam toward two mirrors
    • Blocks half the light for safety

  3. If 4 fringes pass the mark, the mirror moved by two full wavelengths.

    Circle one:   True   False

  4. Gas fills the chamber and 122 fringes pass. What does the count reveal?

    • The refractive index of the gas
    • The color of the laser
    • The thickness of the mirrors

  5. A 630 nm laser is used and 3 fringes pass the mark. Type the mirror shift in nm.

    Answer: ______________

  6. Why does the design take both halves from one source?

    • To double the brightness
    • So the halves stay coherent and fringe
    • To keep the arms the same length

  7. The same gas fills a 4 cm chamber instead of 2 cm. What do you expect?

    • About twice as many fringes pass
    • Half as many fringes pass
    • The same count, width plays no role

  8. A student counts 117 fringes instead of 122 in the gas run. What happens to the result?

    • The index comes out too large
    • Nothing changes, errors cancel
    • The index comes out too small
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Counting fringes to measure tiny shifts W1-mt_Wlb1tZnJBi-s1

  1. One · A half-wavelength move shifts the path by one full wave, so one fringe passes.
  2. Splits one beam toward two mirrors · One beam enters, and half leaves toward each mirror before both return.
  3. True · Each fringe is half a wavelength, and 4 halves make two full wavelengths.
  4. The refractive index of the gas · The fringe count measures the extra waves the gas stacks in, which gives its index.
  5. 945 · Three fringes times half of 630 nm gives a 945 nm shift.
  6. So the halves stay coherent and fringe · Halves from one source keep correlated phases, which stable fringes need.
  7. About twice as many fringes pass · A wider chamber stacks in more waves, so proportionally more fringes pass.
  8. The index comes out too small · A short count means less measured extra path, so the index looks smaller.
Worksheet · LightMySky