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Chapter 32: Problem 54

Find the wavelength of light used in a Michelson interferometer if 550 bright fringes go by a fixed point when the mirror moves \(0.150 \mathrm{mm}\)

Short Answer

Expert verified
The wavelength of the light used in the Michelson interferometer is approximately \(545\) nanometers.

Step by step solution

01

Understand the problem and the formula involved

In the Michelson interferometer, when the mirror moves, bright fringes pass by a certain point. The path difference travelled by the light is then twice the distance the mirror moves (because the light has to travel to the mirror and back). And this path must be equal to the number of fringes times the wavelength. Therefore, from the formula of path difference: \[ 2d = n \lambda\] where: \(d\) is the distance the mirror moves, \(n\) is the number of fringes, and \(\lambda\) is the wavelength of light.
02

Convert the movement distance of the mirror into meters

The value given for the movement distance of the mirror is \[0.150 \mathrm{mm}\], which needs to be converted to meters since the wavelength is generally expressed in meters. Hence, \[d = 0.150 \mathrm{mm} = 0.150 \times 10^{-3}\] meters.
03

Substitute the values into the equation and solve for the wavelength

Substitute \(d\) and \(n\) into the equation \(2d = n \lambda\), and solve for \(\lambda\).\[\lambda = \frac{2d}{n} = \frac{2 \times 0.150 \times 10^{-3} \mathrm{m}}{550} = 5.45 \times 10^{-7} \mathrm{m}\] Therefore, the wavelength of the light is about \(545\) nanometers since \(1 \mathrm{m} = 1 \times 10^{9} \mathrm{nm}.\)

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Most popular questions from this chapter

The CIA wants your help identifying individual terrorists in a photo of a training camp taken from a spy satellite at \(100-\mathrm{km}\) altitude. You ask for details of the optical system used, but they're classified. However, they do tell you that the optics are diffraction limited and can resolve facial features as small as \(5 \mathrm{cm} .\) Assuming a typical optical wavelength of \(550 \mathrm{nm},\) what do you conclude about the size of the mirror or lens in the satellite camera?

The interference pattern from two slits separated by \(0.37 \mathrm{mm}\) has bright fringes with angular spacing \(0.065^{\circ} .\) Find the light's wavelength.

Why don't you see interference effects between the front and back of your eyeglasses?

Find the minimum telescope aperture that could resolve an object with angular diameter 0.35 arcsecond, observed at 500 -nm wavelength. (Note: 1 arcsec \(=1 / 3600^{\circ} .\) )

A double-slit experiment with \(d=0.025 \mathrm{mm}\) and \(L=75 \mathrm{cm}\) uses 550 -nm light. Find the spacing between adjacent bright fringes.
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