A ray of light with wavelength ? air in air is traveling in air and is incident

Question

A ray of light with wavelength ?air in air is traveling in air and is incident on the top surface of a thin film of a material that has

n = 1.3.

Below the film is a flat piece of glass that has

n = 1.9

(see figure below). The film has thickness t.

Which of the following is the correct condition for constructive interference between the rays reflected at the top and bottom of the film?

A ray of light with wavelength ?air in air is traveling in air and is incident on the top surface of a thin film of a material that has n = 1.3. Below the film is a flat piece of glass that has n = 1.9 (see figure below). The film has thickness t. Which of the following is the correct condition for constructive interference between the rays reflected at the top and bottom of the film?

Explanation / Answer

To get constructive interference, the two reflected waves have to be shifted by an integer multiple of wavelengths. This must account for any phase shift introduced by a reflection off a higher-n material, as well as for the extra distance traveled by the wave traveling down and back through the film.

To determine whether these waves interfere constructively or destructively is the fact that whenever light reflects off a surface of higher index of refraction, a 180° phase shift in the wave is introduced.

due to phase shift  we get constructive interference when 2t = (m+1/2)? but

the wavelength changes inside the film to ?n =?/n

so we get constructive interference when 2t = (m+1/2) ?n

or 2nt = (m+1/2)?

here both cases have 180 degree phase change.

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