Question

You are standing in air and are looking at a flat piece of glass (n = 1.52) on which there is a layer of transparent plastic (n = 1.61). Light whose wavelength is 512 nm in vacuum is incident nearly perpendicularly on the coated glass and reflects into your eyes. The layer of plastic looks dark. Find the two smallest possible nonzero values for the thickness of the layer.

smaller value: nm

larger value: nm

Answer 1

Since it is given that the plastic layer looks darker, the path difference condition must have matched with the destructive interference for this plastic layer thickness.

Let us consider,

plastic layer thickness =t nm

refractive index of the plastic layer=n=1.61

wavelength of the incident light==512 nm

The condition for destructive interference,

where, m is the order and has values of 1, 2, 3, ...

So, for the fist two small possible values for thickness are,

Hence the answers are,

smaller values is 79.503 nm and larger value is 238.509 nm.