Question

Light is incident perpendicularly from air onto a liquid film that is on a glass plate. The liquid film is 70.2 nm thick, and the liquid has index of refraction 1.50. The glass has index of refraction 1.40. Calculate the longest visible wavelength (as measured in air) of the light for which there will be totally constructive interference between the rays reflected from the top and bottom surfaces of the film. Assume that the visible spectrum lies between 400 nm and 700 nm.

Answer 1

λ₀ = 421.2 10⁻⁹ m

Step-by-step explanation:

This is an exercise in constructive interference by reflection, let's review some concepts:

* When a ray goes from a medium with a lower index to one with a higher index, it undergoes a phase change of 180º, in this case we have a phase change from the air to the film

* Within the material the wavelength changes according to the spare part index of the material

λₙ = λ₀ / n

By including these two aspects, the constructive interference equation remains

2 n t = (m + ½) λ₀

λ₀ =
`(2nt)/(m+ (1)/(2) )`

we substitute

λ₀ = 2 1.50 70.2 10⁻⁹ / (m + ½)

let's substitute some values ​​of m

m = 0

λ₀ =
`(210.06)/(0.5)` 10⁻⁹

λ₀ = 421.2 10⁻⁹ m

is in the visible range

m = 1

λ₀ =
`(210.6)/(1+0.5)` 10⁻⁹

λ₀ = 140.4 10⁻⁹ m

This outside visible range, is ultraviolet light