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We look at thin film interference.

Interference

Thin films

Suppose there is a very thin film of dielectric and light is incident on it normally. Lets consider single reflections. (We make the small angle ofincidence approximation)

We will assume n 3 > n 2 > n 1 . The physical path length difference of the reflected light is Δ r = 2 d . We will get maxima in the interference when: Δ r = 2 d = m λ 2    m = 1 , 2 , 3 where λ 2 is the wavelength in the film. Now λ i ν i = c / n i . In our example we have ν 1 = ν 2 = ν 3 , that is the frequency does not change moving between the media. So we have λ 1 n 1 = λ 2 n 2 = λ 3 n 3 . Thus constructive interference will happen when λ 2 = λ 1 n 1 n 2 2 d = m λ 2 m = 1 , 2 , 3 . . 2 d = m λ 1 n 1 n 2 2 d = m λ a i r n a i r n f i l m 2 d = m λ 1 1 n f i l m ( 2 d ) n f i l m = m λ a i r m = 1 , 2 , 3 where n f i l m = n 2 . Destructive interference will happen when ( 2 d ) n f i l m = m λ a i r / 2 m = 1 , 3 , 5

When destructive interference occurs then that value of λ is not reflected. Note that this is a function of both d and λ . The next effect is that different colours of light get reflected at differentthicknesses of the film. This is why soap films or oil films on water give rainbow effects.

Note I have assumed that n 3 > n f i l m > n a i r in the above, where n 3 is the material that the film sits upon.

Consider an interface between two materials with indices of refraction n 1 and n 2 . If n 2 > n 1 . Then lets examine what happens to the phase of an electromagnetic wave uponreflection. For a transverse electric field, there is a phase change of π . For the transverse magnetic field (or E ) there is not, if the light ray is close to the normal. However if n 1 > n 2 then and the situation is reversed and the transverse electric field does not undergo a phase change and the transverse magnetic field does. In the exampleabove, their will be no relative phase change between the rays in either case. Either both will change by π or neither will change, depending on the orientation of the E field.

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Source:  OpenStax, Waves and optics. OpenStax CNX. Nov 17, 2005 Download for free at http://cnx.org/content/col10279/1.33
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