Diffraction Grating Maximum Order

[silence98]

Homework Statement

A grating having 1000 lines per mm is illuminated with sodium light of mean wavelength 589.3 nm. Determine the maximum order of diffraction that can be observed.

Homework Equations

dsin([tex]\theta[/tex])=m[tex]\lambda[/tex]

d=slit spacing

The Attempt at a Solution

The order of diffraction is given by m, and m=(dsin[tex]\theta[/tex])/[tex]\lambda[/tex], so i figure m takes a maximum value when sin([tex]\theta[/tex])=1, or when m=d/[tex]\lambda[/tex] but i am not sure if this is correct.
I'd be grateful for any hints.

 

[Stonebridge]

Yes, the angle can't be greater than 90 degrees.
So if you put sin = 1 you will get a value for m that could be, for example, 3.4
This means you could get a 3rd order but not a 4th

 

[silence98]

thanks