Question

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.

Answer 1

λ = 482.05 nm

Step-by-step 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 \theta )/(m)`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