Question

A 230 line/mm grating reveals that a beam of light contains three different wavelengths (660 nm, 560 nm, and 460 nm), at what angle would the first-order, second-order, and third-order peak of the first, second, and third wavelengths, respectively, appear?

660 nm	°
560 nm	°
460 nm	°

Answer 1

given: slit spacing in grating 'd' = 1/230 mm = 10⁶/230 nm = 4347.8 nm;

Now for first wave with 'λ' = 660 nm, the first order (m = 1) peak would apper at:

θ = sin^-1(mλ/d) = sin^-1(1*660/4347.8) = 8.73⁰

Again for the wave with  'λ' = 560 nm, the second order (m = 2) peak would appear at:

θ = sin^-1(mλ/d) = sin^-1(2*560/4347.8) = 14.93⁰

Lastly  for the wave with  'λ' = 460 nm, the third order (m = 3) peak would appear at:

θ = sin^-1(mλ/d) = sin^-1(3*460/4347.8) = 18.51⁰