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

We can use the formula for the diffraction grating:

dsinθ = mλ

where d is the distance between the slits in the grating, θ is the angle between the incident light and the diffracted light, m is the order of the maximum, and λ is the wavelength of the light.

For the first source:

d = unknown
θ = sin^-1(0.350/1) = 20.41°
m = 1
λ = 600 nm

Using the formula, we can solve for d:

d = (mλ) / sinθ = (1 x 600 x 10^-9) / sin(20.41°) = 1.09 x 10^-5 m

For the second source:

d = same as above
θ = sin^-1(0.870/3) = 18.93°
m = 3

Using the formula, we can solve for λ:

λ = (m sinθ) / d = (3 x sin(18.93°)) / (1.09 x 10^-5) = 4.97 x 10^-7 m = 497 nm

Therefore, the wavelength of the light from the second source is 497 nm, which corresponds to answer choice B.

In a Diffraction Grating Experiment,light of 600 Nm Wavelength Produces