A plane wave of monochromatic light falls normally on a uniform thin film of oil which covers glass plate. The wavelength of source can be varied continuously. Complete destructive interference is observed for λ$$=5000A0$$ and λ$$=7000A0$$ and for no other wavelength in between. If μ of oil $$1.3$$ and that of glass is $$1.5$$, the thickness of the film will be

Question

A plane wave of monochromatic light falls normally on a uniform thin film of oil which covers glass plate. The wavelength of source can be varied continuously. Complete destructive interference is observed for λ$$=5000A0$$ and λ$$=7000A0$$ and for no other wavelength in between. If μ of oil $$1.3$$ and that of glass is $$1.5$$, the thickness of the film will be

Infinity Learn · Accepted Answer

In this case, both the rays suffer a  phase change of $$1800$$     and the condition for destructive interference is  $$2nd=(m+12)$$λ$$1$$     $$2nd=(m+32)$$λ$$2$$     ∴$$m+12m+32=$$λ$$2$$λ$$1=50007000=57$$     And $$d=(m+12)$$λ$$12n=2.5$$×$$70002$$×$$1.3$$     $$=6738A0=$$     $$6.738$$×$$10$$−$$5cm$$

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