Reflection Grating Homework Solution

[VVill]

Homework Statement

http://img244.imageshack.us/img244/6852/phys24xy.png

Homework Equations

d=1/N d*sin(theta)=m*(lambda)

The Attempt at a Solution

d=1/1970
d=.0005076

.0005076*sin(theta)=2*600e-9

sin(theta)=.0000012/.0005076

arcsin(.002364)=.135º

*sigh*

 

[hage567]

One thing I see is that when you found d you didn't convert from cm to m, so you have inconsistent units in your equation.

 

[VVill]

d=.0005076cm = .000005076m

.000005076*sin(theta)=2*600e-9

sin(theta)=.0000012/.000005076

arcsin(.2364)=13.7º

Anything else I'm missing, because the answer is not 13.7º?

 

[hage567]

Why do you have m=2? If it is first order I would think it would be m=1.

 

[hage567]

Are you sure you are using the right equation? I think the grating equation you are using is not quite right for the conditions of your problem. The one you are using is a special case where the angle of incidence is normal to the grating. You need to include the angle of incidence in your equation. So your equation would be
d*(sin(theta(m)) - sin(theta(inc))) =m*lamda. where m = ±1 for first order maxima. Anyway see if that helps.