diffraction q

[chiddler]

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A diffraction grating with 8000 lines/cm is illuminated with white light. What is the spectrum of the highest order (ie, max value of m) that includes any portion of the visible spectrum?

A. 1
B. 2
C. 3
D. 4

Answer is C. The relevant equation is

mλ=dsin(&#952😉

where d is lines/m.

Ok so the obvious thing to start out with is do m = dsin(&#952😉/λ because we want to find spectrum of highest order. Now i'm not sure what to plug in for sin nor lambda.

I do have the solution but it feels contrived and I want to get a feel for a more...organic? genuine? thought process.

 

[SaintJude]

It shouldn't matter that you don't have a specific value for the wavenlength of visible light, b/c it's such a small range: 400-700 nm. So coudn't you choose 4x 10 ^ -7 m?

I also know sin (theta) = theta at small angles. Am I close? B/c I don't know what else to do.

 

[chiddler]

It shouldn't matter that you don't have a specific value for the wavenlength of visible light, b/c it's such a small range: 400-700 nm. So coudn't you choose 4x 10 ^ -7 m?

I also know sin (theta) = theta at small angles. Am I close? B/c I don't know what else to do.

Good point about the lambda. But they just set theta = 90, so sin=1. I don't understand why.

 

[SaintJude]

Good point about the lambda. But they just set theta = 90, so sin=1. I don't understand why.

hehe, I guessed that they used theta = 90! B/c that would effectively make the sin 0 just go "away" 😛 and it's unlikely that they would expect you to plug in any other number. I mean what else would you choose sin 0 = 0, sin 45 = 0.7 but random

But
1. that's more of a panic mitigation strategy than an explanation...
2. and sin 90=1, That doesn't get you to m = 3?!

What does the explanation say?

 

[chiddler]

hehe, I guessed that they used theta = 90! B/c that would effectively make the sin 0 just go "away" 😛 and it's unlikely that they would expect you to plug in any other number. I mean what else would you choose sin 0 = 0, sin 45 = 0.7 but random

But
1. that's more of a panic mitigation strategy than an explanation...
2. and sin 90=1, That doesn't get you to m = 3?!

What does the explanation say?

My mistake:

It's m/line, so have to invert that 8000.

m = (1/8000) * 10^-2 / 400 * 10^-9 = ~3

"Since we want the largest m, we choose the smallest wavelength and largest sin."