Question

A tank of gasoline (n = 1.40) is open to the air (n = 1.00). A thin film of liquid floats on the gasoline and has a refractive index that is between 1.00 and 1.40. Light that has a wavelength of 626 nm (in vacuum) shines perpendicularly down through the air onto this film, and in this light the film looks bright due to constructive interference. The thickness of the film is 271 nm and is the minimum nonzero thickness for which constructive interference can occur. What is the refractive index of the film?

Answer 1

Refractive index = 1.15

Step-by-step explanation:

As we know for constructive interference of reflected light the path difference of two reflected light rays must be integral multiple of the wavelength

so here we have

`2\mu t = N\lambda`

now here we know that

`\lambda = 626 nm`

`thickness(t) = 271 nm`

now we have

`2(\mu )(271 nm) = (626 nm)`

`\mu = (626)/(542)`

`\mu = 1.15`