I answered the first part of this question correctly, followed the same procedur

Question

I answered the first part of this question correctly, followed the same procedure for the second and got it wrong. What am I doing wrong?

A) A material with an index of refraction of 1.12 is used to coat glass. The index of refraction of glass is 1.5.
What is the minimum thickness of the coat- ing that will minimize the reflection of light with a wavelength of 5660 °A?
Answer in units of µm
5660/4(1.12) = .1263 micrometers (which was correct)

B)Now assume that the coating’s index of re- fraction is 1.77. Assume that the rest of the system (from the previous question) remains the same.
What is the minimum thickness of the coating needed to minimize the reflection of this light now?
Answer in units of µm

I followed the same procedure:
5660/4(1.77) = .0799 micrometers

This is apparently not the right answer, would love to know what went wrong!
Thanks!

Explanation / Answer

The important point is missed out while working on the problem.

In the first case (refractive index of material is less than that of glass), the reflected light will go 180 degree phase shift from glass and coating. the total trip inside the coat is one half of wavelength and the thickness is

                           t = /4n.

in the second case, the refractive index of the coat is greater than the refractive index of the glass. light reflected from the material will under fo 180 degree phase but light reflected glass will not have any phase transistion and thus the light must travel a full wavelength so the thickness is

                           t = /2 n

                             = 5660x10^-10 / 2 (1.77)

                             = 0.1599m

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