At what angle will the highest order maximum appear for a wavelength 450 nm using a grating with 600 lines per mm?
A)36 $\degree$
B)54 $\degree$
C)81 $\degree$
D)90 $\degree$

Question

Quizplus · Accepted Answer

The formula for the angle of diffraction for a grating is given by sinθ = mλ/d, where m is the order of the maximum, λ is the wavelength of light, d is the spacing between the grooves (given by 1/lines per mm), and θ is the angle of diffraction. Substituting the given values, we get sinθ = (1)(450 nm)/(1/600 lines/mm) = 0.54. Taking the inverse sine, we find θ = 32.8 degrees. However, this angle corresponds to the first order maximum. To find the angle of the highest order maximum, we use the formula m = d sinθ/λ. For the highest order maximum, m = lines per mm. Substituting, we get lines per mm = (1/600 lines/mm) sinθ/(450 nm) = 2.38. This value is between 2 and 3, so the highest order maximum corresponds to m = 2, and the angle of diffraction is sinθ = (2)(450 nm)/(1/600 lines/mm) = 1.08. Taking the inverse sine, we get θ = 61.7 degrees, which is closest to choice B (54 degrees).

At What Angle Will the Highest Order Maximum Appear for a Wavelength