Light of wavelength 520 nm is incident a on a diffraction grating with a slit spacing of 2.20 μm , what is the angle from the axis for the third order maximum?

θ = 45.15°

Explanation:

We need to use the grating equation in this question. The grating equation is given as follows:

mλ = d Sin θ

where,

m = order number = 3

λ = wavelength of light = 520 nm = 5.2 x 10⁻⁷ m

d = slit spacing = 2.2 μm = 2.2 x 10⁻⁶ m

θ = angle from the axis = ?

Therefore,

(3)(5.2 x 10⁻⁷ m) = (2.2 x 10⁻⁶ m) Sin θ

Sin θ = (3)(5.2 x 10⁻⁷ m)/(2.2 x 10⁻⁶ m)

Sin θ = 0.709

θ = Sin⁻¹(0.709)

θ = 45.15°