Taking light collected by the telescope and shine it through a diffraction grating with a 765.5 lines/mm. Using the filter that just the brightest Helium II line. you cast the diffraction grating's diffracted pattern on a screen is 22.000cm away and there are 3 dots, m=-1, m=0 amd m=1. the distances between m=-1 and m=1 is 10.7314.
find the speed of the galaxy moving away from us?
d sin theta =m lambda
The Attempt at a Solution
At first, I think I need to find the angel by using: y_m=Ltan lambda
then I have: 0.22 tan theta _1 =0.107314/2 → theta=47.3972 degrees
Since I have the angel, I can find the wavelength of the light by using: d sin theta =m lambda
then I have: 1mm/765.5 sin (47.3972)= 1*lambda → lambda = 962 nm
I get stuck at this step, can anyone give me a hit to get the answer?