How is the Angular Separation in a Diffraction Grating Calculated?

[WenyiJones]

Homework Statement

A diffraction grating of 3900 slits per centimeter is used to analyze the spectrum of mercury.
(a) Find the angular separation in the first-order spectrum of the two lines of wavelength 579 nm and 577 nm.
(b) How wide must the beam on the grating be for these lines to be resolved?

Homework Equations

dsin(theta)=m*lumda

The Attempt at a Solution

what is the angular separation? Is it just Theta?

 

[Fightfish]

Yes, the angular separation is theta. You might want to read up on the derivation of the equation (if you haven't) so as to better understand it.

 

[Redbelly98]

The way I read the question, angular separation would be the difference between the two angles (thetas) that you would calculate here.

 

[WenyiJones]

the equation i used was:

maximum equation for multi-slit interference
d sin(theta)=m*lamda

d=distance between two slits
m=the interger called the order (bright spots)
theta=angular separation
lamda=wavelength

but when i plugged in numbers, the sin(theta) i got was easily over 1, that is obviously wrong. what's wrong with it?

 

[WenyiJones]

okay, the whole time i was calculating wrong.

it's correct!

how about (b)?

 

[Fightfish]

I should think it has to do with the Rayleigh criterion.