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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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Most popular questions from this chapter

A thin film of oil \((n=1.50)\) is spread over a puddle of water \((n=1.33) .\) In a region where the film looks red from directly above $(\lambda=630 \mathrm{nm}),$ what is the minimum possible thickness of the film? (tutorial: thin film).
A Michelson interferometer is set up using white light. The arms are adjusted so that a bright white spot appears on the screen (constructive interference for all wavelengths). A slab of glass \((n=1.46)\) is inserted into one of the arms. To return to the white spot, the mirror in the other arm is moved $6.73 \mathrm{cm} .$ (a) Is the mirror moved in or out? Explain. (b) What is the thickness of the slab of glass?
White light containing wavelengths from \(400 \mathrm{nm}\) to \(700 \mathrm{nm}\) is shone through a grating. Assuming that at least part of the third-order spectrum is present, show that the second-and third-order spectra always overlap, regardless of the slit separation of the grating.
A pinhole camera doesn't have a lens; a small circular hole lets light into the camera, which then exposes the film. For the sharpest image, light from a distant point source makes as small a spot on the film as possible. What is the optimum size of the hole for a camera in which the film is $16.0 \mathrm{cm}$ from the pinhole? A hole smaller than the optimum makes a larger spot since it diffracts the light more. A larger hole also makes a larger spot because the spot cannot be smaller than the hole itself (think in terms of geometrical optics). Let the wavelength be \(560 \mathrm{nm}\).
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