Final answer:
The wavelength of light used in the Michelson interferometer, resulting in 316 fringes when the mirror was moved by 0.100 mm, is calculated to be 633 nm.
Step-by-step explanation:
The question relates to using a Michelson interferometer to measure the wavelength of light. According to the setup, when the movable mirror is moved by 0.100 mm, 316 fringes are observed moving through. To find the wavelength, we use the relationship given by the formula for a Michelson interferometer: λ = (2 × distance moved) / number of fringes.
A Michelson interferometer is a device used to measure the wavelength of light. In this case, when the movable mirror is moved by exactly 0.100 mm, 316 fringes are observed moving through. To find the wavelength of the light, we can use the equation:
wavelength = (distance moved by mirror) / (number of fringes observed)
Plugging in the values: wavelength = 0.100 mm / 316 fringes = 0.000316 mm or 316 nm (nanometers).
In this case, the distance the mirror moved is 0.100 mm or 0.100 × 10-3 m, and the number of fringes is 316, so:
λ = (2 × 0.100 × 10-3 m) / 316
= 2 × 10-4 m / 316
= 6.33 × 10-7 m or 633 nm.
Therefore, the wavelength of the light used is 633 nm.