A discharge tube is known to produce two spectral lines,one at 640 nm and the other at 640.4 nm.The total number of rulings that a grating must have to just resolve these lines in the second order is
A)400
B)800
C)1600
D)3200
E)6400

Question

Quizplus · Accepted Answer

The resolution of spectral lines using a diffraction grating is determined by the grating equation and the Rayleigh criterion for resolution. According to the Rayleigh criterion, two wavelengths, λ and λ + Δλ, are just resolved in the nth order of diffraction when their diffraction patterns are separated by the angular distance corresponding to the first minimum of one pattern coinciding with the maximum of the other. The formula for the resolving power (R) of a grating is given by R = λ/Δλ = nN, where n is the order of diffraction and N is the total number of rulings on the grating. Given: λ = 640 nm, Δλ = 0.4 nm, and n = 2 (second order).R = λ/Δλ = 640/0.4 = 1600Therefore, nN = 1600. Since n = 2, we find N by rearranging the equation to N = 1600/n = 1600/2 = 800. Thus, the grating must have at least 800 rulings to just resolve these two spectral lines in the second order.

A Discharge Tube Is Known to Produce Two Spectral Lines,one