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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 246 nm and is the minimum nonzero thickness for which constructive interference can occur. What is the refractive index of the film?

Respuesta :

Answer:

Refractive index of film = 1.27

Explanation:

for the constructive interference of reflected light we know that the condition is given as

[tex]2\mu t = N\lambda[/tex]

here we know

[tex]\mu[/tex] = refractive index of the liquid film

t = thickness of layer

t = 246 nm

[tex]\lambda = 626 nm[/tex]

now from the above condition of maximum interference

[tex]2(\mu)(246 nm) = 626 nm[/tex]

[tex]\mu = 1.27 [/tex]