Alaser shined through a diffraction grating with lines that are 1/500 mm apart creates a spectra on a screen. the distance from the center bar to the first side bar is 66 mm. the distance from the diffraction grating to the first side bar is 187 mm. calculate the wavelength of light (in nanometers) that is being emitted by the laser.

To solve this equation we must use the following formula:

λ = d·sinθ/n

λ = wavelength
d = distance between lines of diffraction grating
sinθ = is angle of diffraction
n = order

It may appear we are missing information but we can actually solve this equation. We are told that d = 1/500 mm = 2 x 10⁻⁶ m and n = 1 since we are looking at the first spectral line. Now we must solve sinθ. We are not given any angles, however we are given two distances.

The question is describing a right triangle, where the distance from the center bar to the first line is 66 mm, and this is the side opposite the angle of diffraction. We are also told the length of 187 mm which is the length of the hypotenuse. sinθ = opposite/hypotenuse

Sinθ = 66/187, now we can solve for the wavelength.

λ = (2 x 10⁻⁶)(66/187)/1 = 7.06 x 10⁻⁷ m
λ = 706 nm