A multiple-slit diffraction grating has a slit separation of 1.75 × 10−⁶ m.Find the wavelength of the monochromatic light that will have its second-order bright fringe diffracted through an angle of 36.0°.(1 nm = 10−⁹ m) A)389 nm B)868 nm C)514 nm D)343 nm E)257 nm

Question

Quizplus · Accepted Answer

The formula for the angle of the bright fringe in a multiple-slit diffraction grating is given by:

sinθ = mλ/d

where m is the order of the bright fringe (in this case, m = 2 for the second-order bright fringe), λ is the wavelength of the light, d is the slit separation, and θ is the angle of the bright fringe.

We can rearrange this formula to solve for the wavelength:

λ = md/sinθ

Plugging in the given values, we get:

λ = (2)(1.75 × 10^-16 m)/(sin 36.0°)

Using a calculator, we find:

λ ≈ 514 nm

which corresponds to answer choice C.

A Multiple-Slit Diffraction Grating Has a Slit Separation of 1