Diffraction Grating Angle Between Second Order Maxima

[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.

Homework Statement

“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.”

Homework Equations

nλ = d sin θ

n=2

λ = 6.5 * 10^-6 and 4.0 * 10^-6

d=1/2.5*10^-6

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.

 

[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°