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A diffraction grating is made up of slits of width a with separation d. The grating...

A diffraction grating is made up of slits of width a with separation d. The grating is illuminated by monochromatic plane waves of wavelength λ at normal incidence. What is the angular width of a spectral line observed in the first order if the grating has N slits? State your answer in terms of the given variables. Δθw =

Solutions

Expert Solution

We know from diffraction equations

dsin = m -------------- (1)

for first order, m = 1

The angular width is given as

w = / Ndcos

w = dsin / Ndcos

w = sin / Ncos

from trigonometry, we know that

sin / cos = tan

so

w = tan / N

from equation (1)

dsin =

sin = / d

= arcsin ( / d)

so,

w = tan (arcsin ( / d)) / N

genius_generous answered 3 years ago
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