# Diffraction Grating Angle Between Second Order Maxima

1. May 21, 2013

### Kumo

Hi Everbody,

I am having a bit of trouble with an AS Physics question regarding diffraction gratings. I have managed to solve the problem that I have been facing, although I am not completely sure that I got to it through the correct means, and also why the answer is such.

1. The problem statement, all variables and given/known data

“1. Blue and red light with wavelengths 450nm and 650nm respectively, is inident normally on a diffraction grating which has 4.0 * 105 lines per meter

b) Calculate the angle between the second-order maxima for these wavelengths.”

2. Relevant equations

nλ = d sin θ

n=2

λ = 6.5 * 10-6 and 4.0 * 10-6

d=1/2.5*10-6

3. The attempt at a solution

I attempted the solution two different ways with the first, and to me most intuitive method, failing.

1. sin-1 (2*4.5*10-6)/(2.5*10-6) =θ

θ=21.1°

This was incorrect. However, the following corresponded to the answer at the back of the book.

sin-1 (4.5*10-6)/(2.5*10-6) =θ

θ=10.37°

Now the answer at the back of the book was 10.2°, but I assume that it isn’t the result of sheer chance.

Thank you very much for your time.

2. May 21, 2013

### Kumo

I managed to solve it I think. It turns out that it was a coincidence.

The correct method seems to have been:

(sin-1(2*6.5*10 -7 )/(2.5*10 -6)) - (sin -1 (2*4.5*10 -7)/(2.5*10-6 )) = 10.23°

Last edited: May 21, 2013