# Diffraction grating problem

1. Jan 30, 2006

### twiztidmxcn

Hey

Here is the problem, I think I may be stuck but I'll provide all the information I have so far.

White light (400-700nm) is incident on a 600 line/mm diffraction grating. What is the width of the first order rainbow on a screen 2.0m behind the grating?

What I figured was to use the equation d*sin(theta) = m * wavelength

as well as the equation y = L*tan(theta), with L = 2.0m, m = 1 (first order rainbow),

Basically, I have to find theta, then find y, which ends up being the width of my projected rainbow. I am, however, totally stuck at this point. I'm not even sure if my assumption that m = 1 is right, or if I am on the right path.

Any help in the right direction would be awesome.

Thank you
twiztidmxcn

2. Jan 30, 2006

### finchie_88

This is probably not the best way, but the way that I would do that is to find theta when the wavelength is 400 nm, and then do the same to find the angle when the wavelength is 700 nm, then use a little trig and the difference between the angles to calculate the width of the spectrum.

calculate the angles by using
$$n\lambda = dsin\theta$$ (n = 1, d = distance between the slits).

Last edited by a moderator: Jan 30, 2006
3. Jan 30, 2006

### twiztidmxcn

ok, i had already used that equation for both and found

theta @ 400nm = 13.9 degrees
theta @ 700nm = 24.8 degrees

using the idea of finding the angle difference (10.9 degrees), then using trig we find that tan(theta) = y / x, y = tan (theta) * x, where x = 2m and theta is the angle difference that i calculated?

thus leaving me with something like y = 2m * tan (10.9) = .385m?

Last edited: Jan 30, 2006
4. Jan 30, 2006

### Staff: Mentor

The difference between the angles doesn't help you here because $\tan{\theta_2} - \tan{\theta_1}$ does not equal $\tan (\theta_2 - \theta_1)$.

5. Jan 30, 2006

### twiztidmxcn

I think I get what you mean

It makes more sense with that explanation, and helps me to reason that since x*tan(theta) = y, y2 - y1 = x(tan(theta2)-tan(theta1)).

What you were saying is to use the difference of lengths rather than angle because... well of what you said.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook