A beam of white light (from 400 nm for violet to 700 nm for red) is normally incident on a diffraction grating. It produces two orders on a distant screen. Which diagram below (R = red, V = violet) correctly shows the pattern on the screen?
A) I.
B) II.
C) III.
D) IV.
E) V.

Question

A beam of white light (from 400 nm for violet to 700 nm for red) is normally incident on a diffraction grating. It produces two orders on a distant screen. Which diagram below (R = red, V = violet) correctly shows the pattern on the screen? 
A) I. 
B) II. 
C) III. 
D) IV. 
E) V.

Quizplus · Accepted Answer

The pattern produced by a diffraction grating consists of a central bright maximum with bright spots on either side. The angles of deviation for each order depend on the wavelength of the light and the spacing of the grating. In this case, since we are given that we see two orders on the screen, we know that the angle of deviation for the first order is 30 degrees (sin(30) = 0.5 for the spacing of the grating), and since the beam is normally incident, the angle of incidence is also 30 degrees. Using these angles and the given wavelength range, we can calculate the angular deviation for each color. Red light (700 nm) will be deviated the least, with a deviation angle of sin^{-1}((700 nm)/(2 * 500 nm * sin(30))) = 14.3 degrees, and violet light (400 nm) will be deviated the most, with a deviation angle of sin^{-1}((400 nm)/(2 * 500 nm * sin(30))) = 8.3 degrees. Thus, the central maximum will be white light, with red on one side and violet on the other. The correct diagram is C, which shows the central maximum with red and violet spots on either side.

A Beam of White Light (From 400 Nm for Violet