Question

White light is shone on a very thin layer of glass (n = 1.5), and above the glass layer, interference maxima for two wavelengths (and no other in between) are seen: one green wavelength of 550 nm, and one orange wavelength of 610 nm. What is the thickness of the glass layer?

		1862 nm
		1859 nm
		1860 nm
		1861 nm

Answer 1

t = thickness

for wavelength , ₁ = 610 nm

2t = (m + 0.5)₁/n                      eq-1

for wavelength , ₂ = 550 nm

2t = (m + 1 + 0.5) ₂/n                      eq-2

using eq-1 and eq-2

(m + 0.5)₁/n = (m + 1.5) ₂/n

(m + 0.5) (610) = (m + 1.5) (550)

m = 8

using eq-1

2t = (m + 0.5)₁/n     

2 t = (8 + 0.5) (610)/1.5

t = 1728.33 nm