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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

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?

Some mirrors for infrared lasers are constructed wit alternating layers of hafnia and silica. Suppose you want to produce constructive interference from a thin film of hafnia \((n=1.90)\) on BK-7 glass \((n=1.51)\) when infrared radiation of wavelength \(1.06 \mu \mathrm{m}\) is used. What is the smallest film thickness that would be appropriate, assuming the laser beam is oriented at right angles to the film?

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