## Mastering Physics Solutions: Using a Michelson Interferometer

Using a Michelson Interferometer

Part A = 632.8 nm
Part B = methanol

Solution Below:

You are asked to find the index of refraction for an unknown fluid, using only a laser and a Michelson interferometer. A Michelson interferometer consists of two arms–paths that light travels down, which end in mirrors– attached around a beam splitter. The beam splitter separates the incoming light into two separate beams and then recombines them once they return from the ends of the arms. The recombined beams are sent to a telescope, where their interference pattern may be observed in detail.

Part A

First, you must find the wavelength of the laser. You shine the laser into the interferometer and then move one of the mirrors until you have counted 100.0 fringes passing the crosshairs of the telescope. The extremely accurate micrometer shows that you have moved the mirror by 0.03164 millimeters. What is the wavelength λ of the laser?

The beam has to travel from the splitter to the mirror and back. Since there are 100 spots, the total distance traveled is 100 wavelengths long, so the mirror has moved 100/2 (50) wavelengths. In other words, the following formula applies:

2D = nλ
2 * 0.03164mm = 100 * λ
0.06328mm = 100 * λ
0.0006328 mm = λ

Convert to nanometers and you get the answer: 632.8 nm

632.8 nm

Part B

You now immerse the interferometer in a tank filled with some unknown liquid and carefully align the laser into the interferometer. You move the mirror until you count 100.0 fringes passing the crosshairs of the telescope. The micrometer indicates that the mirror has moved 0.02381 millimeters. What is the mystery fluid?

• water (n = 1.333)
• methanol (n = 1.329)
• ethanol (n = 1.362)
• acetone (n = 1.357)
• isopropyl alcohol (n = 1.375)
• saline (n = 1.378)

Start by using the formula from Part A to find the wavelength of light in the sample:

2D = nλ
2 * 0.02381mm = 100 * λ
0.04762mm = 100 * λ
0.0004762 mm = λ

Convert to nanometers:

λ = 476.2 nm

Now find the index of refraction:

n = λ1 / λ2
n = 632.8 / 476.2
n = 1.32885

Note: you can use the calculator to find the index of refraction, but you’ll have to compare it to the list Mastering Physics gives you to find the name of the sample.

methanol

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