physics plz help

Question

The 546.1 nm line in mercury is measured at an angle of 76.7° in the third-order spectrum of a diffraction grating. Calculate the number of lines per centimeter for the grating.

Answer 1

nλ = d sinθ ⇒ 

 

d = nλ/sinθ

 

n = 3

λ = 546.1 x 10^-9 m

θ = 76.7°

 

Plug in the numbers and get d, then divide 1 cm by d to get the number of lines per cm.  Be careful with units.