Question

Monochromatic light of wavelength 588 nm is incident upon a diffraction grating that contains 8500 lines spread out over a distance of 1.5 cm.

a) What is the line spacing of the grating?

b) At what angle does the 2nd principle maximum occur?

c) If the screen is located a distance of 1.55 m from the grating, what is the linear distance on

the screen that separates the central maximum with the 2nd order principle maximum?

Answer 1

a)

d = 1.5/8500 = 1.765 x 10^-4 cm = 1.765 x 10^-6 m

b)

= wavelength = 588 nm = 588 x 10^-9 m

= angle

for maxima, we have

d Sin = (2 n + 1) (/2)

(1.765 x 10^-6) Sin = (2 (2) + 1) ((588 x 10^-9)/2)

= 56.41 deg

c)

D = screen distance = 1.55 m

y = linear distance on the screen

tan = y/D

tan56.41 = y/1.55

y = 2.33 m