A multiple slit diffraction grating has a slit separation of 2.37 × 10−⁶ m.Find the wavelength of the monochromatic light that will have its second order bright fringe diffracted through an angle of 27.7°.(1 nm = 10−⁹ m) A) 358 nm B) 644 nm C) 551 nm D) 367 nm E) 275 nm

Question

Quizplus · Accepted Answer

We use the formula for the angle of maximum intensity given by

d sinθ = mλ

where d is the slit separation, θ is the angle of diffraction, m is the order of the bright fringe, and λ is the wavelength of light.

For the second order bright fringe, m = 2. Plugging in d = 2.37 × 10^−6 m and θ = 27.7°, we have

(2.37 × 10^−6 m) sin(27.7°) = 2λ

Solving for λ, we get

λ = (2.37 × 10^−6 m) sin(27.7°) / 2 ≈ 5.51 × 10^−7 m

Converting to nanometers, we have

λ ≈ 551 nm

Therefore, the answer is choice C.

A Multiple Slit Diffraction Grating Has a Slit Separation of 2.37