Light is shone on a diffraction grating with d = 1.00 x 10-6 m. The second
order (m = 2) maximum occurs at an
angle of 74.6º. What is the
wavelength of the light IN
NANOMETERS?
[?] nm
Hint: The answer will be between 400 and 700.

    λ = 482.05 nm

Explanation:

The diffraction phenomenon and the diffraction grating is described by the expression

         d sin θ = m λ

where d is the distance between two consecutive slits, λ the wavelength and m an integer representing the order of diffraction

in this case they indicate the distance between slits, the angle and the order of diffraction

         λ = d sin θ / m

let's calculate

         λ = 1.00 10⁻⁶ sin 74.6 / 2

         λ = 4.82048 10⁻⁷ m

Let's reduce to nm

         λ = 4.82048 10⁻⁷ m (10⁹ nm / 1 m)

         λ = 482.05 nm

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