Answer to Question #146742 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

Answer

Equation of m^th order maximum

$d\sin \theta =m\lambda$

$d =\frac{m\lambda}{\sin \theta}=\frac{1\times475\times10^{-9}}{\sin 22^°}$

$d=1268\times10^{-9}m$

lines per centimeter is inverse of spacing

$N=\frac{1}{1268\times10^{-9}m}=7886$ lines