- #1

Oijl

- 113

- 0

## Homework Statement

Light of wavelength 680 nm is incident normally on a diffraction grating. Two adjacent maxima occur at angles given by sin θ = 0.2 and sin θ = 0.3, respectively. The fourth-order maxima are missing.

Slit separation d = 6.8 µm

Slit width a = 1.7 µm

What are the largest, second largest, and third largest values of the order number m of the maxima produced by the grating?

## Homework Equations

((y is wavelength))

[diffraction grating, maxima]: dsinθ=my

[single slit, minima]: asinθ=my

## The Attempt at a Solution

I know, from the previous part of this problem, that d = 4a. So, the equation for maxima for the grating can be rewritten

4asinθ=my

I know that sinθ can at most be 1. Therefore, the equation for greatest m is 4a=my, and this solves where m = 10.

So I know the greatest value of m is 10. But how can I figure the penultimate and antepenultimate values of m? If I decrease m by one, so that m = 9, I have the equation

4asinθ=9y

for which a θ exists that will solve it. And for any m less than 10, there is a θ that will make the statement (4asinθ=my) true.

But the answer is not m = 10, 9, 8. How do I find the other order numbers?