Refraction and Reflection of light

[dangish]

7. (a) A material having an index of refraction n = 1.30 is
used as an antireflective coating on glass with an index of
refraction n = 1.50 as shown.

(i) What is the phase shift for the reflection at the interface
between air and the coating (interface 1)?

(ii) What is the phase shift for the reflection at the interface
between the coating and the glass (interface 2)?

(iii) What minimum thickness must the coating have in order
to minimize reflection of light with wavelength λ = 555 nm?

I thought when something gets reflected it is always 180deg.

any ideas on this one?

 

[jbsteele]

(i) The phase shift for the reflection at the interface between air and the coating (interface 1) is 180°.(ii) The phase shift for the reflection at the interface between the coating and the glass (interface 2) is 180° - (2 × arcsin[n1/n2]) = 180° - (2 × arcsin[1.30/1.50]) = 151.37°.(iii) The minimum thickness of the coating must be λ/(4n) = 555 nm / (4 × 1.30) = 212.5 nm in order to minimize reflection of light with wavelength λ = 555 nm.