21.3. Thin Films http://www.ck12.org
FIGURE 21.15
Incoming wave.FIGURE 21.16
Reflected wave.InFigure21.17, you can see the view of two glass plates, separated at one edge by a fine wire, thus creating a thin
air gap between the slides. (The thickness of the wire and the gap have been greatly exaggerated.) We can show that
the light refracted through a flat piece of glass travels undeflected through the glass for any angle of incidence (see
the link below).
http://demonstrations.wolfram.com/RefractionThroughParallelFaces/
You may remember that this was also the case for light traveling through the center of a converging or a diverging
lens. Again, assuming that the rays travel perpendicular to the surface of the slides, and the air gap width where the
rays reflect isd, we can write
2 d=mλ
for the condition of destructive interference. The light ray (black) shown reflecting at the bottom of the top slide
does not undergo any phase change, since the index of refraction of air is less than the index of refraction of glass.
However, the light ray (green) shown reflecting from the top of the bottom slide does undergo a 180◦phase change,
since the ray reflects off a medium (glass) with a higher index of refraction than which it was traveling (air).
FIGURE 21.17
Thus the condition for constructive interference for this case is
2 d=
(
m+^12)
λCheck Your Understanding
What thickness of oil is required in order to see green light of wavelength 525 nm constructively interfere for order
m=1 (light is normal to the surface), as shown inFigure21.14?
Answer:
According to the figure,noil= 1. 20 and nwater= 1 .33. Therefore, the phase change for the reflected wave off the
oil-water interface (as we described above) is 180◦, but the phase change for the reflection at the air-oil interface is