Question

A jewelry maker has asked your glass studio to produce a sheet of dichroic glass that will appear red for transmitted light and blue for reflected light. You decide that "red light" should be centered at 692.nm and that "blue light" is 519 nm. If you use a MgF2 coating (n = 1.39), how thick should the coating be? nm

Answer 1

SOLUTION :

Given that wave length of the red light is

λ=692 nm

Refractive index of the film is n=1.39

If t is the thickness of the film

The condition for constructive interference in the case of reflection is

2nt=(m+1/2)λ

t=(m+1/2)λ/2n

for m=0 ; t=λ/4n=124.46 nm

for m=1; t=3λ/4n=373.38nm

The wave length of the blue light is λ=519 m

The condition for constructive interference in the case of transmission is

2nt=(m)λ

For m=1 ; t=λ/2n=186.69 nm

For m=2; t=2λ/2n=373.38 nm

Hence the thickness of the film must be 373.38 nm