A ray of light incident on a thin film of thickness ‘t’ gets partially reflected and refracted at A at surface I and thereafter it gets reflected and refracted at B of surface II. The rays after emerging in the first medium interfere. Now the inference will depend upon the path difference between AD and ABC, as beyond CD path difference is zero

                                                  294_interference by thin lens.jpg

Putting (IV) and (V) in (III) we obtain

    Δ x = 2 μt cosr

AD as reflected at a denser medium it suffers an additional path difference λ/2
Total path difference the taken place is

2 μ t cosr –  λ/2

For constructive interference

2μt cos r - λ/2 = μn

>> 2 μt cosr = nλ +λ /2 = (2n + 1) λ/2 maxima

For normal Incidence r =0 >> 2 μt = (2n+1) λ/2 = μn

2 μt cosr - λ/2 = (2n+1) λ/2 >> 2 μt cosr = nλ

For normal incidence 2 μt = nλ

Illustration 6:    White light is incident normally on a glass plate of thickness 0.50 x 10-6 m and index of refraction 1.50. Which wavelengths in the visible region (400 nm - 700 nm) are strongly reflected by the plate?

Solution :    The light of wavelength λ is strongly reflected if the light rays reflected are interfering constructively.
    As we know the condition for constructive interference

1036_solution 2010.jpg

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