A thin transparent film of thickness 3000 `Å` and refractive index 1.5 ud deposited on a sheet made of a metal. Assuming normal incidence of light and also that the film is a plane parallel one, what will be the color of a pot made from this sheet when observed in white light?

Explanation

Coditiions for maximum and minimum intensity in reflected light, in case of thin film interference, are
Maxima: `2 mu t = (2n 1) lambda//2, n = 1, 2,…`
Minima: `2 mu t = n lambda, n = 0, 1, 2, 3,…`
Given: `mu = 1.5 , t = 3000 Å = 3000 xx 10^(10) m`
(normal incidence)
Maxima: `2 mu t = (2 n - 1) lambda//2`
`:. 2 xx 1.5 xx (3000 xx 10^(-10)) = (2n - 1) lambda//2`
or `lambda = (4 xx 1.5 xx 3000 xx 10^(-10))/(2n -1)`
`:. lambda =(18000)/(2n - 1) xx 10^(-10) m`
For `n = 1,lambda = 18000 Å`
`n = 2, lambda = 6000 Å`
`n = 3, lambda = 3600 Å`
and so on
Only `lambda = 6000 Å` for `n = 2` lies in the visible range. Intensity will be minimum for `lambda = 4500 Å` which falls in the violet-blue pat of the visible spectrum.
When observed in white light, the red -orange part will be strongly reflected and the violet-blue part will be quite reduced in intensity. Hence, Colour of the pot will appear to be orange-red.