Critical Angle and Dispersion Standards: 4d Students will be able to identify wave properties such as refraction.

When a wave travels from a low speed medium into a high speed medium… Critical angle is largest angle at which both a reflection and refraction are produced. Incident angles above the critical angle result only in reflections. Incident angles below critical angle give both a reflected and refracted wave. Question: 1) Under what conditions will a wave be absorbed? Under what conditions will it produce a reflected and refracted wave? Under what conditions will it produce only a reflection? What does the critical angle depend upon? Activities: Show picture of experiment and label each with whether reflection and refraction or just refraction occurs. Point out critical angle on 5th picture over and note that refracted ray is directly on boundary. Define critical angle as largest incident angle that produces both a reflection and refracted wave. State that the difference in density between the two mediums determines the critical angle. Small differences result in small angles and large differnces result in large angles. Point out that critical angles only occur when moving from a slow to fast medium

The Fish Example Where should Native American aim arrow? Nearer and deeper than actually appears What does fish see? Inside critical angle sees refracted waves from above water Outside 48 degrees sees reflection of bottom Question: A Native American stands on a river bank with a spear. A fish appears in the water. Should the Native American aim in front, behind or right at the image of the fish? Does the fish appear shallower or deeper than it actually is in the water? Describe what the fish sees when it looks at the surface of the water. Activities: Draw refracted ray of light from fish to Indian. Trace ray above water into water to show that fish appears behind where it actually is. Draw second refracted ray in opposite direction and point out that rays converge above actual location of fish. This indicates that fish will appear shallower than it actually is. To hit fish Indian should aim deeper and iin front of image of fish. Mention that Grizzley bears need to learn this when fishing for Salmon. Now trace rays underwater to above water. Note that the fish would see the Indian higher than he actually is. Also note that at critical angle fish will see bank of lake. In fact fish sees from horizon to horizon in a 48 degree circle centered directly above him. Fish need no necks. Outside this circle the fish sees only reflections from the bottom of the pond since he is looking beyond the critical angle of the water air interface.

Total Internal Reflection Only reflections are produced when wave hits a boundary at an angle greater than the critical angle. Natural substances exhibit TIR Ulexite Polar Bear Fur Man made substances Fiber optic cable Substances have small critical angle Now cheaper than copper and more efficient Question: Under what conditions does total internal reflection occur? Does fiber designed to carry light using TIR have a large or small difference between the speed of light in it and the material that surrounds it? Give some examples of both natural and manmade materials that experience TIR. Activities: Remind students that if wave hits boundary at angle greater than critical angle then it will only be reflected. Some materials have extremely small critical angles so this often happens. We call this total internal reflection or TIR. Demonstration: Ulexite Example: Polar Bear hair Example: Diamond Demo: Lucite tube Example: Fiber optic fountain and cable 5180 conversations versus 8 for traditional cable.

Dispersion Dispersion is the process by which different colors of visible light refract different amounts in a material. In general blue/violet bends best Results in Moon Halos and Glories Results in Rainbows Results in colors you see at edge of a spot light Question: Define dispersion. What color is bent best by most dispersive mediums? What color bends the least? List some dispersive mediums. Activities: Show picture and point out that since violet and blue light are closer to the natural frequency of glass, they are held onto for a bit longer and are bent the most. In other words blue bends best. Point out that this means the colors will be separated with blue on the bottom and red on top. The difference in refraction of different colors is called dispersion. List some phenomena that dispersion is responsible for including Moon halos, glories, rainbows and the colors you see at the edge of a spot light beam.

The Rainbow Question: ) Draw a picture of a rain drop and explain how it separates colors. Which color will appear highest in the sky in a primary bow? Which color appears highest in the sky for a secondary bow? What accounts for this difference? Where do you have to be relative to the sun and rain in order to see a rainbow? Activities: Show slide and point out the primary bow water drop with only one reflection. Note that the red comes out at a higher angle to the horizontal than the blue. Point out on other picture how higher drop will thus give observer red light and lower drops blue. We thus see a bow with red over green over blue. This is called a primary bow. Use tinker toy model to show that bow shape is result of drops at certain angle to observer all producing same color. Go back to first picture and note that secondary bow can form with an extra reflection. In this case blue ends up having larger angle with the horizontal and will come from higher drops. You see blue over red. In second picture show secondary bow drops. Point out that a rainbow involves a reflection and refractions so observer must stand with sun at back and rain ahead on him.

Rainbow Continued Must be between rain and sun with sun at back Primary Bow Drops at top give red Lower drops give blue Secondary Bow Higher drops give blue, lower red Extra reflection Point out Alexander’s dark band and that 2ndary bow is wider than primary Show slides if have time.