Calculating Wavelength of Red Line in Hydrogen Spectrum

[gleeson.tim]

A transmission diffraction grating with
520 lines/mm is used to study the line spec-
trum of the light produced by a hydrogen
discharge tube. The grating is 1.6 m from the source (a hole
at the center of the meter stick). An observer
sees the first-order red line at a distance yred =
0.326983 m from the hole.
The speed of light is 2.998 × 108 m/s and
the Planck’s constant is 6.626 × 10−34 J · s.
Calculate the wavelength of the red line in
the hydrogen spectrum. Answer in units of
m.

The Attempt at a Solution

I've tried this many times, this is what I did most recently.

1) a= 1/ # lines / m
2) arc tan ( y red / the grating) = b
3) (a) sin (b) = answer

 

[Redbelly98]

The Attempt at a Solution

I've tried this many times, this is what I did most recently.

1) a= 1/ # lines / m
2) arc tan ( y red / the grating) = b
3) (a) sin (b) = answer

That looks right, now you just need to plug in the numbers. Watch the units, since the problem statement did use "mm" for one of the quantities.