**Using a Michelson Interferometer**

Part A = 632.8 nm

Part B = methanol

**Solution Below:**

Part A

Express your answer in nanometers, to four significant figures.

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

- 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 = λ_{1} / λ_{2}

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