A 4.00-cm wide diffraction grating with 250 grooves per cm is used to resolve two closely spaced lines (a doublet)in a spectrum.The doublet consists of two wavelengths,$\lambda$_a = 629.8 nm and $\lambda$_b = 630.2 nm.The light illuminates the entire grating at normal incidence.What order of diffraction is required to resolve these two lines using this grating?

Question

Quizplus · Accepted Answer

The spacing between adjacent grooves on the grating is d=1/250 cm. The angle between the central maximum and the first-order maximum for a diffraction grating is given by sinθ=nλ/d, where n is the order of diffraction. For the first-order maximum to resolve the doublet, the angle between the two peaks must be greater than the angular width of the peaks. This angular width can be approximated as the width of one peak divided by the distance between the peaks, or Δθ≈(4 cm)/(630.2 nm-629.8 nm). Substituting this into the equation for the first-order maximum and solving for n, we get n=2. Therefore, the answer is (C) 2.

A 400-Cm Wide Diffraction Grating with 250 Grooves Per Cm Is