An oil film covers the surface of a small pond. The refractive index of the oil is greater than that of water. At one point on the film, the film has the smallest non-zero thickness for which there will be destructive interference in the reflected light when infrared radiation with wavelength 800 nm is incident normal to the film. When this film is viewed at normal incidence at this same point, for what visible wavelengths, if any, will there be constructive interference? (Visible light has wavelengths between 400nm and 700 nm )

Explanation

Ray-1 is reflected from denser medium and ray-2 from denser medium.
` (##DCP_V05_C32_E01_051_S01.png" width="80%">
`:. Deltax = 2mut = lambda = 800nm` for destruction interference.
` mut = 400nm `
For constructive interference ,
` Deltax = 2mut = (2n-1) lambda/2`
` :. lambda = ((4mut)/(2n-1))= ((1600)/(2n-1))`
For `n=1, lambda=1600nm `
For `n=2, lambda = 533nm`
For `n=3, lambda = 320 nm`
The only wavelength lying in the given range is
533 nm.