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Chapter 34: Problem 65

A Michelson interferometer is illuminated with a 600.-nm light source. How many fringes are observed if one of the mirrors of the interferometer is moved a distance of 200. \(\mu \mathrm{m} ?\)

Short Answer

Expert verified
Answer: 667 fringes.

Step by step solution

01

Convert distance and wavelength to the same units

In this problem, the wavelength is given in nanometers and the distance the mirror is moved is given in micrometers. To make calculations easier, let's convert both values to meters: Wavelength (\(\lambda\)) = 600 nm = 600 * 10^{-9} m Distance mirror is moved (d) = 200 μm = 200 * 10^{-6} m
02

Calculate path difference

The path difference is the difference in distance traveled by the light in the two arms of the interferometer. Since the light reflects back and forth in one arm, the path difference is equal to twice the distance the mirror is moved: Path difference (PD) = 2 * d = 2 * (200 * 10^{-6} m) = 400 * 10^{-6} m
03

Calculate the number of fringes

To find the number of fringes observed, we need to determine how many full wavelengths of the light source fit into the path difference. We can do this by dividing the path difference by the wavelength: Number of fringes (N) = PD / \(\lambda\) = (400 * 10^{-6} m) / (600 * 10^{-9} m)
04

Simplify and find the final answer

Now, we just need to simplify the expression and find the number of fringes: N = (400 * 10^{-6} m) / (600 * 10^{-9} m) = (400 / 600) * (10^3) N = (2 / 3) * 1000 N = 666.67 Since the number of fringes must be a whole number, we can round the result to the nearest integer. Therefore, the number of fringes observed is 667.

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Most popular questions from this chapter

In a double-slit experiment, He-Ne laser light of wavelength \(633 \mathrm{nm}\) produced an interference pattern on a screen placed at some distance from the slits. When one of the slits was covered with a thin glass slide of thickness \(12.0 \mu \mathrm{m},\) the central fringe shifted to the point occupied earlier by the 10 th dark fringe (see figure). What is the refractive index of the glass slide? (a) Without the glass slide (b) With glass slide

Light of wavelength \(653 \mathrm{nm}\) illuminates a slit. If the angle between the first dark fringes on either side of the central maximum is \(32.0^{\circ},\) What is the width of the slit?

Coherent monochromatic light passes through parallel slits and then onto a screen that is at a distance \(L=2.40 \mathrm{~m}\) from the slits. The narrow slits are a distance \(d=2.00 \cdot 10^{-5} \mathrm{~m}\) apart. If the minimum spacing between bright spots is \(y=6.00 \mathrm{~cm},\) find the wavelength of the light.

In a single-slit diffraction pattern, there is a bright central maximum surrounded by successively dimmer higher-order maxima. Farther out from the central maximum, eventually no more maxima are observed. Is this because the remaining maxima are too dim? Or is there an upper limit to the number of maxima that can be observed, no matter how good the observer's eyes, for a given slit and light source?

Two different wavelengths of light are incident on a diffraction grating. One wavelength is \(600 . \mathrm{nm}\) and the other is unknown. If the 3 rd order of the unknown wavelength appears at the same position as the 2 nd order of the \(600 . \mathrm{nm}\) light, what is the value of the unknown wavelength?
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