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Chapter 32: Problem 53

A Michelson interferometer uses light from glowing hydrogen at \(486.1 \mathrm{nm} .\) As you move one mirror, 530 bright fringes pass a fixed point in the viewer. How far did the mirror move?

Short Answer

Expert verified
By performing the above calculations, one would obtain the distance the mirror moved in meters.

Step by step solution

01

Convert the wavelength to meters

To convert the given wavelength from nanometers to meters, use the conversion factor \(1 \mathrm{m} = 10^{9} \mathrm{nm}\). Thus, the wavelength \( \lambda \) in meters is given by\[ \lambda = 486.1 \times 10^{-9} \mathrm{m} \].
02

Determine the total path difference

The total path difference is obtained by multiplying the wavelength of the light by the number of fringes observed, which is given by\[ \text{Total Path Difference} = n \times \lambda = 530 \times 486.1 \times 10^{-9} \mathrm{m} \].
03

Find the mirror movement

Since the light makes a round trip, the distance the mirror moves is half the total path difference, calculated as\[ \text{Mirror Movement} = \frac{\text{Total Path Difference}}{2} \].

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Most popular questions from this chapter

Find the angular position \(\theta\) of the second-order bright fringe in a double-slit system with 1.5 - \(\mu\) m slit spacing if the light's wavelength is (a) \(400 \mathrm{nm}\) and (b) \(700 \mathrm{nm}\).

One arm of a Michelson interferometer is \(42.5 \mathrm{cm}\) long and is enclosed in a box that can be evacuated. The box initially contains air, which is gradually pumped out. In the process, 388 bright fringes pass a point in the viewer. If the interferometer uses light with wavelength \(641.6 \mathrm{nm},\) what's the air's refractive index?

Green light at \(520 \mathrm{nm}\) is diffracted by a grating with 3000 lines/cm. Through what angle is the light diffracted in (a) first and (b) fifth order?

Find the minimum angular separation resolvable with \(633-\mathrm{nm}\) laser light passing through a circular aperture of diameter \(2.1 \mathrm{cm} .\)

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