Physics 200 Class #3 Notes




September 14, 2005
Completion of Chapter 1 of Text
Chapter 2
Class Exercises
Introduction to the lab
{Review Scientific Notation and Significant Figures in External Links (Blackboard)}
{Homework #1}
A bit more on refraction:
Brief note on index of refraction: n.
The amount of light that reflects from the interface between two materials depends on several
factors - the angle of incidence, the orientation of the electric field vector, and the speed of light in
the different materials. That's right, light has different speeds in different materials, with its
maximum speed in a vacuum. This will be covered more in chapter 2, but this is a quick peek
ahead. The index of refraction actually tells you how much slower light moves in a certain
material than light moves in a vacuum.
n = speed of light in a vacuum / speed of light in the material
n=c/v
Gradual change of index of refraction
On the interface between two media with different indices of refraction, the change in the direction
of the light occurs over a very short distance. On the other hand, when the index of refraction of a
medium changes gradually, the refraction is continuous and the light may gradually bend.
One example is seen in mirages. On a hot day, there is a layer of hot air near the ground, with
cooler, denser air above it. Since light travels faster in the less dense, hot air, light bends slightly
upwards making it seem as if the ground is reflecting. This may also fool people into thinking
there is water on the ground reflecting.
Phy 200 Fall 2005 Class_3
Page 1 of 9
from: http://hypertextbook.com/physics/waves/refraction/mirage-illinois.jpg
Phy 200 Fall 2005 Class_3
Page 2 of 9
http://virtual.finland.fi/netcomm/news/showarticle.asp?intNWSAID=25722
Continuation of Chapter 1 How Light Behaves
Review of first 7 “Observations”
1: Light travels in a straight line so long as it moves through a single uniform substance.
2:
(a) The angle of reflection equals the angle of incidence.
(b) The incident ray, the reflected ray, and the normal lie in the same plane
3: Light paths are reversible
4: On the transition from air to water, the angle of refraction is less than the angle of incidence.
5: In refraction, the ratio of sines is the same for all angles of incidence (but the ratio depends on
the pair of materials).
6: The relative index of refraction depends on the pair of substances.
7: When the angle of incidence exceeds the critical angle, the light beam is totally reflected.
Intersection:
Consider two searchlights intersecting in the sky. What about two laser beams of the same color? Two
laser beams of different color. (Demonstrations)
Observation 8. Light beams can intersect without perceptible effect
1.2 The speed of light in vacuum
Newton (Opticks 1704) calculated the time for light from the sun to reach the earth by using the value
of the speed calculated by Roemer (1676). Roemer measured the delay in the termination of the
eclipses of one of Jupiter’s moons six months apart. The eclipse was observed 16.6 minutes late due
to the light traveling the extra distance gained between the earth and jupiter in 6 months.
Phy 200 Fall 2005 Class_3
Page 3 of 9
Estimation:
speed of light in vacuum=
diameter of earth's orbit
3 x1011 m

 3.3 x108 m / s
apparent delay in eclipse termination
900 s
Currently accepted value is very close to 3 x 108 m/s (186,000 mi/s). This is the speed of light in
empty space. We need to consider the speed in materials in more detail in Chapter 2.
1.3 White Light and Colors
Note Figures 1.10-1.12 carefully.
In class demonstrations and lab, we notice that blue light is refracted at a greater angle than red
light.
Observation 9. White light consists of a mixture of all colors of the rainbow.
Observation 10. The index of refraction is different for different colors of light.
We use the latter property to build devices to analyze light (Lab #3 Prism Spectrometer).
Example: For glass the index of refraction for “red” light is 1.514 and the index of refraction for
“blue” light is 1.529. We will be more specific later about what we mean by red light and blue
light. For now, just think about the two ends of the visible spectrum of colors. This very small
change (~ 1%) is large enough to “spread” the spectrum and to make a useful device for analyzing
light...
Rainbows: dispersion of light by refraction in water drops. The light first refracts upon entering
the water drop, then reflects off the back surface, then refracts when coming back out into the air.
The refraction is different for different color light, so get separation of the colors. The most
intensity of the light is at 42 degrees from the incoming light.
Below: a graphic representation, the ray path in the water drops:
Phy 200 Fall 2005 Class_3
Page 4 of 9
And how it looks when the light comes from many water drops. You look in the sky and see a
rainbow. ROY G BIV
your eye:
Phy 200 Fall 2005 Class_3
Page 5 of 9
Why 42 degrees?
Concentration of light around the maximum angle, 42 degrees from the incoming light. That is,
the light is most intense at 42o from the direction of the sunlight. This covers an arc in the sky
from your point of view.
Phy 200 Fall 2005 Class_3
Page 6 of 9
from: http://physics.uwstout.edu/WX/u15/U15_06.gif
from: http://www.alanbauer.com/photogallery/Water/Rainbow%20over%20Case%20InletHorz.jpg
Phy 200 Fall 2005 Class_3
Page 7 of 9
1.4 Sidedness
Note: The author likes to use the word “sidedness” for the phenomenon that we are about to
discuss. The more common term is “polarization”. In order to describe this behavior, we will use
Polaroid sheets (invented in the late 1930s). Newton did not have these sheets, but he did have a
naturally occurring material that produces the same effect on light. These “sidedness” phenomena
had been known for centuries using single crystals of calcium carbonate (Calcite). It is simply
easier to work with Polaroid sheets.
The text describes the production of these sheets. The important thing to remember is that a special
direction has been embedded in the plastic, the direction of the stretching and alignment. You
should be able to state in your own words what happens in the following exercises.
1. Place a single sheet in front of a source of light.
2. Place another sheet on top of the first with their “stretch directions” parallel to one another.
3. Hold the first sheet fixed and rotate the top sheet slowly. What happens as we turn the top sheet
through an angle of 180 degrees? Be specific as the angle changes from zero to 90 degrees and
then from 90 degrees to 180 degrees.
The light between the two sheets must have some sort of sidedness or rotating the top sheet would
have no effect.
Phy 200 Fall 2005 Class_3
Page 8 of 9
Although not discussed in the text, we might do the following experiment:
With the two stretch directions at right angles to each other, place a third sheet between the two
sheets and vary the direction of its stretch direction. An acceptable model for light must be able to
explain the results of these experiments.
Observation 11. Light has some kind of “sidedness”.
1.5 Variations in Intensity (“Thin film effect”)
Brief discussion and demonstration
Observation 12. When light of a single color falls on a thin film, the patterns of reflected and
refracted light show a complex (non-uniform) and often beautiful pattern.
1.6 The Rainbow
Brief discussion and demonstration
General ideas:
(a) Ray path in the raindrop
(b) Light is concentrated near a return angle of 42 degrees
Phy 200 Fall 2005 Class_3
Page 9 of 9