For this problem, you will only be concerned with the geometric aspects of thin-film interference, so ignore phase shifts caused by reflection from a medium with higher index of refraction. (Because of the structure of a butterfly's wings, such phase shifts do not contribute much to what you actually see when you look at the butterfly.) Part A Assume that light is incident normal to the surface of a film of thickness d. How much farther does the light reflected from the back surface travel than the light reflected from the front surface

This is a problem is interference by reflection, where it is requested not to take into account the changes of phase and change in the wavelength within the film

λₙ = λ₀ / n

When the wave enters the film, it must reach the end of the film, be reflected and reach the initial surface, therefore the total length is

d = 2 t

where t is the thickness of the film, because the film is perpendicular to the surface

therefore the difference in optical path between the reflected ray on the surface and the end film is

Λ = 2 t