A thin film of plastic `(n=1.56)` is `0.25mum` thick. It is sandwiched between two glass slabs with refractive indice of `1.58` and `1.52` respectively White light (400-700nm) is first incident normally on the slab for which `n=1.58` Which visible wavelength (in nm) is missing in the reflected light?

Answer

`520 nm`

Explanation

`2tmu=(n+1/2)lambda` (for destructive interference)
`Rightarrow2tmu=(n+1/2)lambda`
`Rightarrow 2t(1.56)=(n+1/2)lambda`
`Rightarrow 2xx0.25xx10^(-6)xx1.56=(n+1/2)lambda`
`:.(n+1/2)lambda=7.8xx10^(-7)=780nm`
`lambda=780/(n+1/2)`
`n=0,lambda=1560` nm
`n=1, lambda=1560/3=520` nm
`n=2,lambda=780xx2/5=312`nm(not possible)