Questions: The Michelson Interferometer

Question 1

In a Michelson interferometer lit by a 633 nm laser, one mirror is moved 0.100 mm. About how many fringes pass a fixed point?

• A. About 158
• B. About 316
• C. About 632
• D. About 1580

Answer: (B)

Each fringe corresponds to a mirror shift of λ/2. N = 2Δd/λ = 2 × 1.00 × 10⁻⁴ m / 6.33 × 10⁻⁷ m ≈ 316.

Question 2

Moving one mirror of a Michelson interferometer by half a wavelength shifts the fringe pattern by exactly one fringe.

• T. True
• F. False

Answer: True

The beam goes to the mirror and back, so a shift of λ/2 changes the round-trip path by λ, which restores the same interference condition one order over.

Question 3

What did Michelson and Morley set out to detect in 1887?

• A. The wavelength of sodium light
• B. Earth's motion through a supposed light-carrying ether
• C. The speed of light in water
• D. Gravitational waves

Answer: (B)

They expected the time for light to travel along and across Earth's direction of motion through the ether to differ. They saw no such shift, a result later explained by special relativity.

Question 4

An empty gas cell of length L sits in one arm. As gas is let in, N fringes pass. Write the refractive index n of the gas in terms of N, L, and the vacuum wavelength λ.

Model answer: n = 1 + Nλ/(2L)

The cell is crossed twice, so the optical path changes by 2L(n − 1). Each fringe is one wavelength of change: 2L(n − 1) = Nλ.