Question

ou find that you really do not like a certain shade of color in yellow when it reflects off of the glass (n = 1.50) floor in your (expensive) house . So, you decided coat that floor with a material with index of refraction n = 1.38 in order to eliminate light beams of wavelength λ = 550 nm, when is reflected off of the glass and the coating perpendicular to the surface. What is the smallest thickness of the coating that is required for your wish?

Answer 1

To eliminate light of particular wavelength, there should be destructive interference between the light reflected from top and bottom surface of film. As at both reflecting surfaces, refractive index of medium below the surface is more than that of medium above the surface, condition of destructive interference is standard condition, that is optical path difference = (2m-1)*wavelength/2. Where m is an integer.

Optical path difference = 2nt

where n is refractive index of film and t is its thickness. Hence

2tn = (2m-1)* Lamda/2

For minimum possible value of t, m should be minimum, that is 1. Hence

t(minimum) = Lamda/4n = 550 nm /4*1.38

= 100 nm = 10^-4 mm