Answer:
λ₀= 495.88 nm
Explanation:
To analyze this constructive interference interference experiment by reflection, let's look at two important aspects:
* when a ray of light passes from a medium with a lower index, they refact to another medium with a higher index, the reflected ray has a phase difference of pyres
* When a beam penetrates a material medium, the wavelength of the radiation changes according to the refractive index of the material.
λₙ = λ₀ / n
when we introduce these aspects in the expression of contributory interference, it remains
2 d sin θ = (m + ½) λ₀ / n
In general, reflection phenomena are measured at an almost normal angle, whereby θ = π/2 and sin θ = 1
2 d = (m +1/2) λ₀/ n
2n d = (m + ½) λ₀
Let's apply this expression to our case
d = (m + ½) λ₀ / 2n
Suppose we measure on the first interference, this is m = 0
d = ½ λ₀ / 2n
let's calculate
d = ½ 496 10⁻⁹ / (2 2.30)
d = 53.9 10-9 m
This is the thickness of the glass, the next wavelength that gives constructive interference is
λ₀ = 2 n d / (m + ½)
let's calculate
λ₀ = 2 2.3 5.39 10-8 / (1 + ½)
λ₀= 4.9588 10-7 m
λ₀= 495.88 nm
