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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