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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 grating is made of exactly 8000 slits; the slit spacing is $1.50 \mu \mathrm{m} .\( Light of wavelength \)0.600 \mu \mathrm{m}$ is incident normally on the grating. (a) How many maxima are seen in the pattern on the screen? (b) Sketch the pattern that would appear on a screen \(3.0 \mathrm{m}\) from the grating. Label distances from the central maximum to the other maxima.
In a double-slit interference experiment, the wavelength is \(475 \mathrm{nm}\), the slit separation is \(0.120 \mathrm{mm},\) and the screen is $36.8 \mathrm{cm}$ away from the slits. What is the linear distance between adjacent maxima on the screen? [Hint: Assume the small-angle approximation is justified and then check the validity of your assumption once you know the value of the separation between adjacent maxima.] (tutorial: double slit 1 ).
Parallel light of wavelength \(\lambda\) strikes a slit of width \(a\) at normal incidence. The light is viewed on a screen that is \(1.0 \mathrm{m}\) past the slits. In each case that follows, sketch the intensity on the screen as a function of \(x\), the distance from the center of the screen, for $0 \leq x \leq 10 \mathrm{cm}$ (a) \(\lambda=10 a\). (b) \(10 \lambda=a,\) (c) \(30 \lambda=a.\)
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.
The radio telescope at Arecibo, Puerto Rico, has a reflecting spherical bowl of \(305 \mathrm{m}(1000 \mathrm{ft})\) diameter. Radio signals can be received and emitted at various frequencies with appropriate antennae at the focal point of the reflecting bowl. At a frequency of \(300 \mathrm{MHz}\), what is the angle between two stars that can barely be resolved? (Tutorial:radio telescope).
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