Find the angle in degrees for the third-order maximum for 577 nm wavelength yellow light falling on a diffraction grating having 1,420 lines per centimeter.

θ = 0.14°

Explanation:

Here we will use the grating equation. The grating equation is as follows:

mλ = d Sin θ

where,

θ = angle = ?

m = order number = 3

λ = wavelength of light = 577 nm = 5.77 x 10⁻⁷ m

d = spacing between slits = 1/(1420 lines/cm) = 7.042 x 10⁻⁴ m

Therefore, using these values, we get:

(3)(5.77 x 10⁻⁷ m) = (7.042 x 10⁻⁴ m)Sin θ

Sin θ = (3)(5.77 x 10⁻⁷ m)/(7.042 x 10⁻⁴ m)

Sin θ = 2.46 x 10⁻³

θ = Sin⁻¹(2.46 x 10⁻³)

θ = 0.14°

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