Need help with a diffractiongrating problem.

[seanmcgowan]

Homework Statement

Light with a wavelength of 400nm passes through a 1.00x10^4 lines/cm diffraction grating. What is the second order angle of diffraction?

a) 21.3 c)56.5
b) 53.1 d) 72.1

Homework Equations

d*sin(theta)=m* wavelength

The Attempt at a Solution

I rearranged the equation to: Theta= sin^-1({wavelength*order}/ d)
Theta= sin^-1 (4*10^-7*2/{1/1*10^2)= sin^-1(8*10^-9)= 4.58366

Obviously, this isn't the answer. Could someone show me how to figure these problems out? I have a test coming up and i am completely stumped on all of these types of questions.

 

[rl.bhat]

Theta= sin^-1 (4*10^-7*2/{1/1*10^2)= sin^-1(8*10^-9)= 4.58366

Here d = 0.01/1x10^4 m or 10^-6 m.

 

[seanmcgowan]

Ok i reworked the problem, and got a different answer, but it is still no where near any of the multiple choice answers! what am I doing wrong?

 

[Redbelly98]

Can you show your second calculation, with the new value of d? Otherwise we can't see what's wrong.

EDIT:

4*10^-7*2/(1/1*10^2) = 8*10^-9

There is an error here, besides the incorrect value of d. Do you see it?

 

[seanmcgowan]

Holly cow! I just re-reworked the problem for about the hundredth time and got the answer of 53.1, which is actually one of my choices! and I should imagine that the (8*10^-9) is wrong. The answer should be 8*10^-1. Right? or am I STILL messing up?

 

[Redbelly98]

Yes, it is 0.8 using the correct value of d=10^-6m.

Or, if d=(1/10²)m or 10^-2m as you had earlier, you should have gotten 8x10^-5 for the expression.