Suppose a piece of glass is coated with a thin layer of another material, and
I send light toward it (Figure 36-12). The sources of the two rays of light
are the reflection from the top layer, and the reflection from the boundary.
This animation (http://users.erols.com/renau/thinfilm.html)
(requires Shockwave) shows the waves coming in.
There are two sources of phase difference:
(1) Optical Path Length difference between rays, where
optical path length = (index of refraction)*(physical
path length)
(2) Phase introduced upon reflection:
If light is in a material of higher index, and reflects from a boundary with
a material of lower index, phase change of 0 , "Hi off lo change of zero",
and conversely, "Lo off hi, change of pi" and we can focus
on the phase angle or call it a change of 1/2 wavelength.
In this course, we will always use waves which are incident perpendicular to
the surface (called “normal incidence”), so the angle
of incidence will be zero (it is measured from the normal).
1. Set your simulation so the incoming waves make an angle of almost
90 deg.with the surface -- not exactly 90 deg. because we want to be able to
see both waves.
(a) Try dragging the thick bar separating the blue film from the gray
glass and see the interference change from constructive to destructive.
What is the smallest thickness (in number of wavelengths) of the “blue”
film that gives fully constructive interference? Focus on the red line which
is where the two rays are at the same point.
What is the path difference in this case? How many wavelengths in the film is this?
(b) What is the next thickness (in number of wavelengths) of the “blue”
film that gives fully constructive interference? Focus on the red line which
is where the two rays are at the same point.
What is the path difference in this case? How many wavelengths in the film is
this?
(c) How does the wavelength in the “blue film” compare to the wavelength in air?
Recall that the index of refraction n = c / v:
• is the speed of light in the film faster or slower than
in air?
• is the frequency of light in the film larger or smaller
than in air?
• So, must the wavelength of light in the film be longer or shorter
than in air?
Write the relationship between the wavelength in air lambda0 and
the wavelength in the film lambdaf.
(d) Look at the indices of refraction again:
• Was the light reflecting off the air-film interface (the top reflection)
reflecting off the more dense or the less dense
material?
What was its phase change? 0 pi
? (Circle one.)
• Was the light reflecting off the film-glass interface (the lower reflection
--where the line is thick) reflecting off the more dense or the
less dense material?
What was its phase change? 0 pi
? (Circle one.)
• What is the total phase difference due to reflection?
0 pi ? (Circle one.)
2. In this case, what thickness of the film will give fully destructive
interference?
3. Now change the index of refraction of your film. What effect did this
have on your answers to the questions above?
(a)
(b)
(c)
(d) When you changed to the more dense film:
• Was the light reflecting off the air-film interface (the top reflection)
reflecting off the more dense or the less dense
material?
What was its phase change? 0 pi
? (Circle one.)
• Was the light reflecting off the film-glass interface (the lower reflection
--where the line is thick) reflecting off the more dense or the
less dense material?
What was its phase change? 0 pi
? (Circle one.)
• What is the total phase difference due to reflection?
0 pi ? (Circle one.)
4. In this case, what thickness of the film will give fully destructive
interference?
This page maintained by Anne G. Young. Last modified 29-Apr-2003 .