A diffraction grating has 450 lines per mm.What is the highest order m that contains the entire visible spectrum from 400 nm to 700 nm?
A) m = 2
B) m = 3
C) m = 4
D) m = 5
E) m = 6

Question

Quizplus · Accepted Answer

The highest order m that contains the entire visible spectrum is given by the formula nλ = d sinθ for bright spots, where n is the order, λ is the wavelength of light, d is the spacing between the grating lines, and θ is the angle of diffraction. Since we want the entire visible spectrum to diffract, we need to find the angle θ that will result in the longest wavelength (700 nm) being diffracted at the edge of the spectrum. Using the formula θ = sin^-1(nλ/d), we can solve for n when θ is equal to the inverse sine of 700 nm and d is equal to 1/450 mm. We get n = 3.03, which means that the third order (m=3) diffraction maxima will contain the entire visible spectrum.

A Diffraction Grating Has 450 Lines Per Mm