Question

A thin oil slick (no=1.50) floats on water (nw=1.33). When a beam of white light strikes this film at normal incidence from air, the only enhanced reflected colors are red (650 nm) and violet (390 nm). From this information, deduce the (minimum) thickness t of the oil slick.

Answer 1

The (minimum) thickness of the oil slick is 325 nm.

Step-by-step explanation:

Let the (minimum) thickness of the oil slick =
`t_(o)`

Therefore:

2
`t_(o)` = (
`m_(red)`+
`(1)/(2)`)*λ
`_(red)`/
`n_(o)` (1)

similarly,

2
`t_(o)`=(
`m_(violet)+(1)/(2)`)*λ
`_(violet)`/
`n_(o)` (2)

Thus, equation 1 = equation 2

(
`m_(red)`+
`(1)/(2))`*λ
`_(red) /n_(o)` = (
`m_(violet)+(1)/(2))`*λ
`_(violet)/n_(o)`

Where:

λ
`_(red) = 650 nm`

λ
`_(violet) = 390 nm`

`n_(o) = 1.5`

Therefore:

`(2m_(violet)+1 )/(2n_(red)+1 )`=650/390=5/3

This shows that,

`m_(violet)`=2

`m_(red)`=1

Thus, using equation 2

`t_(o)`=
`(5*390)/(2*2*1.5) =325 nm`