Final answer:
A Michelson interferometer can be used to measure the expansion coefficient of a rod. By connecting one end of the rod to a mirror and keeping the other mirror fixed, the fringes observed in the interferometer will change as the rod expands due to heating. The expansion coefficient can be calculated using the equation ε = Δl / (l0 · ΔT). The central fringe moves by a certain number of times, which can be calculated using the given wavelength of light.
Step-by-step explanation:
The expansion coefficient of a rod can be determined using a Michelson interferometer. In this case, the rod is connected to one of the mirrors, while the other mirror is fixed. As the rod expands due to heating, the fringes observed in the interferometer will change.
To calculate the expansion coefficient of the rod, we can use the formula:
ε = Δl / (l0 · ΔT)
where:
- ε is the expansion coefficient
- Δl is the change in length of the rod
- l0 is the initial length of the rod
- ΔT is the change in temperature
In this case, the length of the rod is given as 20 cm and its expansion rate is given as 50 micrometers due to a temperature change of 50 degrees. We can now substitute these values into the formula to find the expansion coefficient. Using the given wavelength of light of 500 nm, we can also calculate how many times the central fringe moves.