Optics - Thin Film

Consider two horizontal glass plate with a thin film of air between them. For what values of the thickness of the film of air will the film, as seen by reflected light, appear bright if it is illuminated normally from above by blue light of wavelength 488 nanometers?

A. 0, 122 nm, 244 nm
B. 0, 122 nm, 366 nm
C. 0, 244 nm, 488 nm
D. 122 nm, 244 nm, 366 nm
E. 122 nm, 366 nm, 610 nm
(GR9677 #82)
Solution:

See Thin Film.

Glass to Air: n n→ Δ= 0
Air to Glass: n n→  Δ= 2t  λ

Δ = Δ− Δ= 2t  + ½λ

Blue Light → Constructive Interference: Δ =
→  =  2t  + ½λ
→ t = ½λ(m − ½)
with λa = 488 nm and m = 0,1,2,3...
m = 1 →  t = ½λ(1 − ½) = ¼ λ = 122 nm
m = 2 →  t = ½λ(2 − ½) = ¾ λ = 366 nm
m = 3 →  t = ½λ(3 − ½) = ⁵/4 λ = 610 nm

Answer: E

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