Question

Light of a single wavelength is incident on a diffraction grating with 500 slits/mm. Several bright fringes are observed on a screen behind the grating, including one at 45.9 ∘ and one next to it at 73.2∘.

What is the wavelength of the light?

Answer 1

λ (wavelength)=478nm

Step-by-step explanation:

Given Data

diffraction grating with 500 slits/mm.

∅₁=45.9°

Ф₂=73.2°

λ=?

Solution

dSin∅₁=nλ

dSinФ₂=(n+1)λ

then

λ=d(Sin∅₁-SinФ₂)

where d=1/500

d=
`2*10^(-6)m`

λ=
`2*10^(-6)(Sin(73.2)-Sin(45.9))`

λ=
`4.783*10^(-7)m`

λ=478nm