Mastering Physics Solutions: Multiconcept Exercise 24.65

Exercise 24.65

Part A = 2 Click to use the calculator/solver for this part of the problem

Solution Below:

A diver under water is looking at the overhead Sun through a diffraction grating that has 7000 lines/cm.

Part A

What is the highest complete spectrum order that can be seen by the diver?
Express your answer as an integer.

Use the following formula:

dsin(θ) = nλ

We know how much Mastering Physics sucks, and this problem is no exception. Since it doesn’t tell you the wavelength to use for visible light, you could get the wrong answer here. Some references give a value of 850 nm for the wavelength of red light (the longest in the visible spectrum), but it seems like Mastering Physics wants you to use 740 nm. Also, since the diver is under water, you have to consider the refractive index of water (1.33). So dividing 740 nm by 1.33 gives you a λ of 556 nm, so plug that in. The sun is overhead, so θ is 90 degrees. Finally, d is just the grating separation. To find it, first convert the grating to meters: 7000 slits per cm is 700,000 slits per meter. Then take 1 / 700,000, which equals 0.0000014286.

dsin(θ) = nλ
n = d * sin(θ) / λ
n = 0.0000014286 * sin(90) / (556 * 10^-9)
n = 2.53

Since the problem asks for the highest *complete* spectrum order, you have to round *down*, to 2:

n = 2


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