Two flat plates of glass with parallel faces are on a table, one plate on the ot

Question

Two flat plates of glass with parallel faces are on a table, one plate on the other. Each plate is 10.8 cm long and has a refractive index of 1.55. A very thin sheet of metal foil is inserted under the end of the upper plate to raise it slightly at that end, in a manner similar to that pictured in the figure (Figure 1). When you view the glass plates from above with reflected white light, you observe that, at 1.14 mm from the line where the sheets are in contact, the violet light of wavelength 401 nm is enhanced in this reflected light, but no visible light is enhanced closer to the line of contact. x_green, 2 = 4.68 mm x_, 2 = 5.84 mm How thick is the metal holding the ends of the plates apart?

Explanation / Answer

as the visible light is not enhanced at the point of contact, that means that the visible light undergoes phase reversal after the reflection from bottom plate
now, for the 401 nm enhancement, the plate seperation be t
then, 2n*t = m*lambda
n = 1.55 given
for m = 1
t = 401*10^-9/2*1.55 = 129.354*10^-9 m

so from ratio proporion, if foil thickness is D
t/1.14 = D/108
D = 1.225*10^-5 m

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