A plane wave of monochromatic light falls normally on a uniform thin film of oil which covers a glass plate. The wavelength of source can be varied continuously. Complete destructive interference is observed for l $$=$$ $$5000$$ Å and l $$=$$ $$7000$$ Å and for no other wavelength in between. If m of oil is $$1.3$$ 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 a glass plate. The wavelength of source can be varied continuously. Complete destructive interference is observed for l $$=$$ $$5000$$ Å and l $$=$$ $$7000$$ Å and for no other wavelength in between. If m of oil is $$1.3$$ 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 $$180$$∘ and the condition for destructive interference is: $$2nd=(m+12)$$λ$$12nd=(m+32)$$λ$$2$$,∴$$m+12m+32=$$λ$$2$$λ$$1=50007000=57and$$ $$d=(m+12)$$λ$$12n=2.5$$×$$70002$$×$$1.3=6738$$Å$$=6.738$$×$$10-5cm$$.

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