# Interference in thin films

#### logearav

Joined Aug 19, 2011
243
Members, kindly see my attachment.
A ray of monochromatic light AB is incident on the surface K of film. It is partly reflected along BC and partly refracted into the film along BD. At the point D on the surface K', the ray of light is partly reflected along DE and partly transmitted out of the film along DG. The reflected light then emerges into air along EF which is parallel to BC.
In my attachment ZX is the normal drawn. So,<ABZ is angle of incidence.
<ZBC----angle of reflection;
Now my question is how <ABZ and <MEB are equal? Both are designated as 'i' in the attachment. Because, angle between incident ray and normal drawn qualifies to be angle of incidence. There is no incident ray in the triangle MEB.

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#### Georacer

Joined Nov 25, 2009
5,182
$$\hat{ABZ}=\hat{ZBM} =90^o-\hat{MBE} =90^o-(180^o-\hat{BME}-\hat{MEB}) =\hat{MEB}$$

#### ErnieM

Joined Apr 24, 2011
8,055
Another way, <ABZ = <ZBM (by angle of incidence = angle of reflection)

As Z-X is a perpendicular, <ZBE = 90 (right angle)

Therefor: <MBE = 90 - <ZBM = 90 - <ABZ

For right triangle BME:
<MEB = 90 - <MBE = 90 - (90 - <ABZ)

<MEB = <ABZ