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Chapter 25: Problem 11

The Michelson Interferometer A Michelson interferometer is adjusted so that a bright fringe appears on the screen. As one of the mirrors is moved \(25.8 \mu \mathrm{m}, 92\) bright fringes are counted on the screen. What is the wavelength of the light used in the interferometer?

Short Answer

Expert verified
Answer: The wavelength of the light used in the Michelson interferometer is approximately \(5.61 \times 10^{-7}\) meters, or \(561 \, \mathrm{nm}\).

Step by step solution

01

Write down the given information

We're given that the mirror is moved \(25.8 \mu \mathrm{m}\), and there are 92 bright fringes counted. This means \(\Delta L = 25.8 \times 10^{-6}\) meters, and \(m = 92\).
02

Rearrange the formula to solve for the wavelength

We need to find \(\lambda\). To do this, we can rearrange the formula for the Michelson interferometer fringe shift: $$\lambda = \frac{2\Delta L}{m}$$
03

Plug in the given values and solve for the wavelength

Now, we can plug in the values for \(\Delta L\) and \(m\): $$\lambda = \frac{2(25.8 \times 10^{-6})}{92}$$ $$\lambda = \frac{51.6 \times 10^{-6}}{92}$$ $$\lambda = 5.61 \times 10^{-7} \mathrm{m}$$
04

Write the final answer

So, the wavelength of the light used in the Michelson interferometer is approximately \(5.61 \times 10^{-7}\) meters, or \(561 \, \mathrm{nm}\).

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