Question

A material with an index of refraction of 1.11 is used to coat glass. The index of refraction of glass is 1.5. What is the minimum thickness of the coating that will minimize the reflection of light with a wavelength of 5240 ˚A?

answer in units of µm. Please explain how you know it is destructive interference, even though both undergo a 180 phase change.

Answer 1

In order to minimize the reflection of light, we need destructive interference between the ray that is reflected from the outer surface of the coating and the ray that is reflected from the coating - glass interfece. And the optical path difference between the two rays should be such that the condition for destructive interference occurs.
  Now, the optical path difference is
  
where, d is the thickness of the coating and n_c is the index of refraction of the coating.
And the condition for destructive interference is such that the path difference is
    (We are considering only the case of minimum thickness) .
So, we require