White light containing wavelengths from 400 nm to 750 nm falls on a grating with 8500 lines/cm. How wide is the first-order spectrum on a screen 2.50 m away?
1 Answer
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sin theta = lambda/d = (400×10^-9)/(0.01/8500) = 0.34 or theta = 19.88 degrees
theta1 for lambda = 750 nm = sin^-1[(0.34×750)/400] = sin^-1[0.6375] or
theta1 = 39.61 degrees
Width of spectrum would be 2.50[tan 39.61 – tan 19.88] = 1.165 m
