A uniform thin film of material of refractive index 1.40 coats a glass plate of refractive index 1.55. This film has the proper thickness to cancel normally incident light of wavelength 525 nm that strikes the film surface from air, but it is somewhat greater than the minimum thickness to achieve this cancellation. As time goes by, the film wears away at a steady rate of 4.20 nm per year. What is the minimum number of years before the reflected light of this wavelength is now enhanced instead of cancelled?

31.25 year .

Explanation:

The thickness of layer must change so the destructive interference may be converted into constructive interference . This can happen if thickness is reduced by λ /4 , so that path difference changes by 2 x   λ /4 =  λ /2 .

This will convert destructive to constructive interference.

change in thickness required = λ /4

= 525 / 4 nm

= 131.25 nm .

year required to wear off

= 131.25 / rate of decay

= 131.25 / 4.2

= 31.25 year .

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