Question

Diffraction gratings with 10,000 lines per centimeter are readily available. Suppose you have one, and you send a beam of white light through it to a screen 2.00 m away. Find the angles for the first-order diffraction of the shortest and longest wavelengths of visible light (380 and 760 nm).

Answer 1

The angles for the first-order diffraction of the shortest and longest wavelengths of visible light are 22.33 ⁰ and 49.46 ⁰ respectively.

Angle for the first order diffraction

The angle for the first order diffraction is calculated as follows;

dsinθ = mλ

sinθ = mλ/d

For shortest wavelength (λ = 380 nm)

d = 1/10,000 lines/cm

d = 1 x 10⁻⁴ cm x 10⁻² m/cm = 1 x 10⁻⁶ m/lines

sinθ = (1 x 380 x 10⁻⁹)/(1 x 10⁻⁶)

sinθ = 0.38

θ = sin⁻¹(0.38)

θ = 22.33 ⁰

For longest wavelength (λ = 760 nm)

sinθ = (1 x 760 x 10⁻⁹)/(1 x 10⁻⁶)

sinθ = 0.76

θ = sin⁻¹(0.76)

θ = 49.46 ⁰

Learn more about diffraction here: brainly.com/question/16749356

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