Answer to Question #284532 in Optics for luna

Question

Problem: Find the minimal resolving power of the diffraction grating (lattice) if it enables

us to resolve the two spectral lines of potassium (λ1 = 578 nm and λ2 = 580 nm). How

many minimal numbers of strokes (slits) (N) should have this grating that the resolving is

possible in the spectrum of the second order.

Answer 1

$R=\frac{\lambda_1+\lambda_2}{2(\lambda_2-\lambda_1)}=\frac{578+580}{2\cdot(580-578)}=289.5,$

$R=mN,\implies N=\frac Rm=\frac{289.5}2=144.$