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?

a. 1862 nm

b.1859 nm

c. 1860 nm

d.1861 nm

Answer 1

Refractive index of ice n = 1.31

Condition for interference maxima:

Thickness of the layer t = (λ/2n)[m + (1/2)]

                                           Here λ = wave length

                                                   m = 0, 1, 2, 3, .......

For violet :

Thickness of the layer t = (λ/2n)[m + (1/2)]

For m = 2,   t = [550*10^-9 m/(2*1.5)] (2 + (1/2)]

                     = 4.58*10^-7 m

For Red :

Thickness of the layer t = (λ/2n)[m + (1/2)]

For m = 1,  t = [(610*10^-9 m/(2*1.5)] [1 + (1/2)]

                     = 3.05*10^-7 m

Hence thickness of the glass layer t = [(4.58*10^-7 m) + (3.05*10^-7 m)]/2

                                                   = 3.81*10^-7 m