Two glass plates are arranged as in the following figure so that light reflected

Question

Two glass plates are arranged as in the following figure so that light reflected from the bottom surface of the top plate interferes with light reflected from top surface of the bottom plate. As one moves along the x-axis, the total reflected intensity alternates between bright and dark fringes. If there are a total of 22 bright fringes across the entire width of the plates, what is the plate spacing d at the right edge? Assume the source of illumination is blue light with a wavelength of 430 nm.

Explanation / Answer

d = .(p.d.) cos ,……..[1]

(p.d.)sin = m,……..[2]

where,
path difference: p.d.
inclination angle:
# of bright fringes: m = 22
wavelength of incident light: = 430x10^-9 m

Snell’s law:

n’sin = n sin ’……..[3]

where,
refractive index of glass: n’ = 1.4
refractive index of air: n = 1
angle of refraction at glass-air interface:
angle of incidence: ’ = 90 deg.

1.4 sin = 1 sin 90

= arcsin{1/1.4} = arcsin{0.7143} = 45.58 deg.

Solving [1] for p.d. and substituting into [2];

(d/cos)sin = 21

d tan = 22,

d = 22/(tan ) = 22*430x10^-9 / tan45.58

d =9.27038x10^-6 m = 9.27 um.............Ans.

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