Archived Spectrometer CCD Homework: Calculate Spectral Range for m=4

[woaini]

Homework Statement

A spectroscopist has a spectrometer equipped with a grating with 600 grooves/mm. This grating puts a 1228 nm wavelength range on a spectroscopic plate (a CCD) in order m = 5. The spectroscopist now changes the spectroscopic plate CCD by one that is larger by a factor of 3. What spectral range will be accepted when the spectroscopist observes the lines in order m = 4 with the new, larger spectroscopic plate?

λ1=1228
d= 1666.67
m1=5
m2=4
λ2=?

Homework Equations

mλ=dsinθ

The Attempt at a Solution

sinθ=[(5)(1228)]/(1666.67)=3.68

However I can't solve for θ, and plug it into another question for m2=4. What step should I do next?

So what exactly does the electroscopic plate do?

 

[drvrm]

wavelength range on a spectroscopic plate (a CCD) in order m = 5. The spectroscopist now changes the spectroscopic plate CCD by one that is larger by a factor of 3.

i think the first set of data gives you an idea of angle at which the experiment is being done - my guess is that angle of diffraction gives you size of CCD detector.
if you use a larger size you may get a larger coverage of wave length /order of diffraction.