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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
The mirror in the Michelson interferometer moved by a distance of approximately 0.128 mm.

Step by step solution

01

Understand the Problem

The problem asks for the distance that the mirror in a Michelson interferometer has moved if it has caused 530 bright fringes to be observed. This means that for each bright fringe, the mirror has moved by half the wavelength of the used light source. This happens because an increase (or decrease) in the path length by a full wavelength results in constructive interference 鈥� a bright fringe.
02

Convert Wavelength into meters

The wavelength of the light from hydrogen is given in nanometers (nm). For the calculation we need the wavelength in meters (m). So, first of all, the given wavelength needs to be converted into meters, remembering that 1 nm = \(1 \times 10^{-9}\) m. Hence, the wavelength \(\lambda = 486.1 nm = 486.1 \times 10^{-9} m\).
03

Calculate Distance moved by the Mirror

Each bright fringe corresponds to the mirror moving half the wavelength of the light. Thus, the total distance that the mirror moved which has given the 530 bright fringes can be calculated by multiplying the number of fringes by half the wavelength, i.e. \(d = N \times \frac{\lambda}{2}\) where \(N\) represents the number of fringes. Substituting the given values \(N = 530\) and the calculated value \(\lambda = 486.1 \times 10^{-9} m\) gives the total distance that the mirror moved.

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Most popular questions from this chapter

A double-slit experiment has slit spacing \(0.12 \mathrm{mm}\). (a) What should be the slit-to-screen distance \(L\) if the bright fringes are to be \(5.0 \mathrm{mm}\) apart when the slits are illuminated with 633 -nm laser light? (b) What will be the fringe spacing with 480 -nm light?

You're investigating an oil spill for your state environmental protection agency. There's a thin film of oil on water, and you know its refractive index is \(n_{\mathrm{oll}}=1.38 .\) You shine white light vertically on the oil, and use a spectrometer to determine that the most strongly reflected wavelength is \(580 \mathrm{nm}\). Assuming firstorder thin-film interference, what do you report for the thickness of the oil slick?

Find the total number of lines in a 2.5 -cm-wide diffraction grating whose third-order spectrum puts the 656 -nm hydrogen- \(\alpha\) spectral line \(37^{\circ}\) from the central maximum.

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

Find the intensity as a fraction of the central peak intensity for the second secondary maximum in single-slit diffraction, assuming the peak lies midway between the second and third minima.
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