By an anodizing process, a transparent film of aluminium oxide of thickness `t = 250` nm and index of refraction `n_(2) = 1.80 ` is deposited on a sheet of polished aluminium What is the color of utenslis made from this sheet with observer in white light? Assume normal incidence of the light.

Explanation

We must find which colours in the visible region, having vacuum wavelengths from 400 nm (violet) to 700 nm (red), will interfere constructively and which destructively. From the problem, with `n_(1) = 1` (air) maximum constructive interference occurs for
`lambda = (2(n_(2)//n_(1))t)/(m + (1)/(2)) = ((900 nm))/(m + (1)/(2)`
`(m = 0, 2,...`
Only the value corresponding to `m = 1`, that is, `lambda_(1) = 450 nm` (violet) is the visible range.
we infer that the red-orange-yellow end of the spectrum will be strongly reflected, while the violet-blue end will be greatly diminished in intensity as compared with the illumination white light.