INTERFERENCE OF LIGHT REFLECTED FROM A MIRROR:

Rigol J. Ph.D.

Science Department

Cooper City High School

ABSTRACTS:

When the light is reflected on a mirror under an angle θ, most of the light is reflected at an angle θ but as a matter of fact, the light is reflected in all directions. In particular, some light is reflected at an angle θ=0o. The proportion of light reflected in this direction is very small, but using the phenomenon of interference it is easy to observe the effect. That is what we do in this work.

DESCRIPTION:

Trying to replicate the Michelson experiment about the interference of light, I collected lasers, mirrors, splitters and so on. When trying to align the mirrors, I observed some clear patterns of interference, even without using the beam-splitter. With these patterns of interference as a background, it is difficult to find the real Michelson’s interference. I observed these interferences with different mirrors and using lasers with different wave lengths (See inside the rectangles in figs.1-3). Observe that the screen is in the same side as the laser and not at the side of the mirror as, for example, in the case of the Fresnel’s double mirror interference1.

 Fig.1 Fig.2 Fig.3

Usual mirrors are made of a metallic film covered by a plastic or a glass. So I decided to use just a metallic mirror without any cover. The result was clear, there is no interference. It is an indication that the observed interferences are a consequence of the superposition of beams reflected from at least two surfaces. One surface is the metal the other could be or the surface of the glass closer to the metal or the one that is farther.

The investigation of the reflection of the laser beam by a metallic mirror covered by a piece of glass allowed me to observe the following effects:

1-) The center of the circles of interference is always about the middle point between the laser and the spot showing the reflection of the laser beam on the screen.

2-) Increasing the distance laser-mirror very smoothly does not change the pattern of interference.

3-) Increasing the distance mirror-screen, increases the diameter of the circles, but it does not change the pattern of interference, so the increase is just geometry.

4-) Changing the angle laser-mirror, changes dramatically the distribution of dark-bright circles.

5-) Pushing slightly the mirror with one finger changes the alternation dark-bright circles dramatically making the diameter of the circles bigger.

All of these results can be explained assuming that the interference is created by the superposition of light reflected on the mirror with light reflected on the surface of the glass closer to the mirror so the distance glass-mirror should be critical.

To test this hypothesis, I prepared a sandwich made of a 1.00 mm glass and the metal mirror separated by an aluminum paper with thickness d=19.4 μm with a hole in the middle to let the laser beam go through. The geometry of the experiment is shown in fig.4 .

 Fig.4

Using a distance mirror-screen (L=0.50m) and lasers of different colors (λ) we expect that the distance between two consecutive maximums (or minimums) could be calculated by the approximate formula:   ΔX= .

The expected values for ΔX calculated for the different wave lengths are shown on the table:

 COLOR λ (10-9 m) ΔX(m) Expected BLUE 420 0.0108 GREEN 532 0.0137 RED 670 0.0170

As you can see in figs 5-7, the experimental results are consistent with the expected values:

 Fig.5 Fig.6 Fig.7

To check for the effect of the thickness of the glass, I repeated the experiment for the green light using two glasses in the sandwich. The result is shown in the next graph:

 Fig.8

The result is similar to the one obtained using only one glass. That is an indication that the two beams that interfere are the one reflected on the metal and the one reflected on the surface of the glass closer to the metal.

ANALYSIS:

What I find more interesting is that the interference pattern shows circles with the center located between the directions of the incident beam and the reflected beams. That is different from the interference we observe in thin films like soap or oil films where fringes or lines are observed. So, Why circles? There should be a center of symmetry. This is similar to the Newton’s rings, but in our case there is not a lens with a center of symmetry. Also, the glass is not pressed with a sharp object like in ref.2.

We can explain our result assuming that the points of reflection on the mirror and on the glass act as a source of coherent light (see figure below).  So these two beams satisfy the conditions for interference: coherence and the same wave length.

 Fig.9

Evidently for an angle of incidence of the light θ, most of the light will be reflected under an angle θ. But If Feynman was right (see ref.3) the light can be reflected under any angle. So (though small) part of the light can be reflected from both surfaces under an angle zero. If this is correct, then this is why we observe that kind of circular symmetry. Even more, if you play with the mirror at different angles, you will find other patterns with circles with smaller distance between maximums (or minimums) which corresponds to bigger values of “d”. In the experiment it appears like a fine structure (see fig.10). That happens when the light is reflected more than one time between the mirror and the glass. In the particular case when there is one more reflection, the value of “d” is 3 times bigger, and the distance between equivalent circles 3 times smaller.

 Fig.10

As a matter of fact all of these results can be expected as a consequence of the Feynman’s description of the behavior of the light (see ref.4). However, I could not find any reference to this kind of experimental results anywhere.

References

1. Eugene Hecht, “Optics”, Addison-Wesley Publishing Company (2nd Edition),1990, page 344

2. Eugene Hecht, “Optics”, Addison-Wesley Publishing Company (2nd Edition),1990, page 352

3. Richard P.Feynman, The strange theory of light and matter. Princeton Science Library,(2006), page 40.

4. Richard P.Feynman, The strange theory of light and matter. Princeton Science Library,(2006), page 70.