Diffraction grating: In a diffraction grating experiment, light of 600 nm wavelength produces a first-order maximum 0.350 mm from the central maximum on a distant screen. A second monochromatic source produces a third-order maximum 0.870 mm from the central maximum when it passes through the same diffraction grating. What is the wavelength of the light from the second source?
A) 479 nm
B) 497 nm
C) 567 nm
D) 749 nm
E) 794 nm

Question

Quizplus · Accepted Answer

For the first source:
d*sin(theta) = m*lambda
where d is the slit separation, theta is the angle of diffraction, m is the order of diffraction and lambda is the wavelength.
At central maximum, sin(theta) = 0
So, for the first-order maximum,
0.35*10^-3 = (1)(600*10^-9)d
d = 0.5833*10^-3 m
For the second source:
At the same angle of diffraction theta, the path difference between the slits for the second source will be 2*2*d = 4d (as the order of diffraction is 3).
So, for the third-order maximum,
0.87*10^-3 = (3)(lambda)*d/(4d)
lambda = 497*10^-9 m = 497 nm.

Diffraction Grating: in a Diffraction Grating Experiment, Light of 600