Question

The movable mirror of a Michelson interferometer is attached to one end of a thin metal rod of length 23.3 mm. The other end of the rod is anchored so it does not move. As the temperature of the rod changes from 15°C to 25C, a change of 14 fringes is observed. The light source is a He Ne laser, λ=632.8nm. What is the change in length of the metal bar, and what is its thermal expansion coefficient?

Answer 1

To calculate the change in length of the metal bar in a Michelson interferometer and its thermal expansion coefficient, you can use specific formulas. The change in length can be found using ΔL = ΔN * λ / (2 * cosθ), and the thermal expansion coefficient can be found using α = (ΔL / L0) / ΔT.

Step-by-step explanation:

In a Michelson interferometer, the change in length of the metal bar can be calculated using the formula:

ΔL = ΔN * λ / (2 * cosθ)

Where:
ΔL is the change in length of the bar,
ΔN is the change in the number of fringes observed (14 in this case),
λ is the wavelength of the laser light (632.8 nm),
and θ is the angle between the bar and the direction of the laser light.

To calculate the thermal expansion coefficient, we can use the formula:

α = (ΔL / L0) / ΔT
Where:
α is the thermal expansion coefficient,
ΔL is the change in length of the bar,
L0 is the initial length of the bar,
and ΔT is the change in temperature.

Using the given information, we can substitute the values into the formulas to find the change in length of the bar and its thermal expansion coefficient.