A multiple slit diffraction grating has a slit separation of 2.00 × 10−⁶ m.Find the wavelength of the monochromatic light that will have its second order (m = 2)bright fringe diffracted through an angle of 43.4°.(1 nm = 10−⁹ m) A) 616 nm B) 500 nm C) 687 nm D) 120 nm

Question

Quizplus · Accepted Answer

We can use the formula for the diffraction angle for a multiple slit diffraction grating:

sinθ = mλ/d

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

We are given d = 2.00 × 10^(-16) m and θ = 43.4° for m = 2. We can convert this angle to radians:

θ = 43.4° = 0.758 radians

Substituting into the formula and solving for λ:

sin(0.758) = 2λ/(2.00 × 10^(-16))

λ = (sin(0.758))(2.00 × 10^(-16))/2

λ ≈ 6.87 × 10^(-7) m = 687 nm

Converting to the given units:

λ ≈ 68.7 × 10^(-9) m = 68.7 nm

The closest answer choice is (C) 687 nm.

A Multiple Slit Diffraction Grating Has a Slit Separation of 2.00