A diffraction grating has 12, 600 rulings uniformly spaced over 25.4 mm. It is i

Question

A diffraction grating has 12, 600 rulings uniformly spaced over 25.4 mm. It is illuminated at normal incidence by yellow light from a sodium vapor lamp. This light contains two closely spaced lines (the well-known sodium doublet) of wavelengths $89 nm and 589.59 nm. At what angle will the first order maximum occur for the first of these wavelengths? A diffraction grating is of width 5 cm and produces a deviation of 22 degree in the second order with light of wavelength 580 nm. Calculate the slit spacing.

Explanation / Answer

grating spacing:

d = l/N = 25.4X10-3 / 12600 = 2.016x10-6 m

for first order maxima, the angle is,   

angle = sin-1[m*lambda / d]

= sin-1[(+/-)1*589x10-9 / 2.016x10-6]

= (+/-) 16.98o

= (+/-) 17o (approximately)

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