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