Answer to Question #147485 in Optics for Promise Omiponle

Question

Suppose the first-order maximum for 475 nm blue light being transmitted through a diffraction grating is at an angle of 22°.

Randomized Variables
λ = 475 nm
θ = 22°


How many lines per centimeter are there on this diffraction grating?

Answer 1

λ = 475 nm $= 475 \times 10^{-9} \;m$

Equation for m^th order maximum:

dsinθ = mλ

d – separation between lines on grating

$d = \frac{mλ}{sinθ} \\ d = \frac{1 \times 475 \times 10^{-9}}{0.3746} \\ = 1.268 \times 10^{-6} \;m \\ = 1.268 \times 10^{-4} \;cm$

Number of lines per centimeter (N) of grating:

$N = \frac{1}{d} \\ N = \frac{1}{1.268 \times 10^{-4}} = 7886$

Answer: 7886