Solve Unknown Wavelength from Diffraction Grating Homework

[jesuslovesu]

Homework Statement

A grating with 3000 lines per cm is used to disperse green light (500nm) and another light of unknown wavelength on a screen 2 m from the grating. The linear separation between the green and unknown light on the screen in the second order is found to be 10 cm. Find the wavelength of the unknown light.

Homework Equations

$$dsin(\Theta) = m\lambda$$
$$y = m*\lambda*L/d$$

The Attempt at a Solution

L = 2 m
d = 1/300,000 m
y = .1 m
I don't know what the answer is but all I can get is 83 nm by doing this:
.1 m * 300,000 m / 2m / 2 = $$\lambda$$

I am guessing it's wrong because it's not visible light. Does anyone know if I did anything wrong? I'm not sure if I need to do something with the given 500 nm.

 

[hage567]

I think you need to make use of the 500 nm. Try finding y for the 500 nm wavelength. You know that y for the unknown wavelength is 10 cm away from y for the 500 nm.

 

[runphysics]

two step problem
Get y for the green first,using the 500
then add the y + 0.1 meter to get the spread for the other color
Although from the question, I could not tell if you use y +.1 or y-.1
Then solve for wavelength of other color

Maybe one of them gives a bad answer.

 

[hage567]

I was taking it to mean y for the unknown wavelength was further away from the centre, but the question is a little vague.