Transcript Rainbows
Rainbows Jeremy Neal Liquid Crystal Institute Kent State University Introduction The following topics will be covered: • The physics of rainbow formation. • Different types of rainbows, including: – – – – Single Rainbows Multiple Rainbows Circular Rainbows Reflection Rainbows • Other interesting rainbow effects, including: - Supernumerary Arcs - Sky Darkening between Rainbows • Interesting rainbow facts. Background Information •Natural light is made up of a mixture of different wavelengths. The spectrum is almost continuous across the visible range. •Light from the sun can be considered to be coming in parallel by the time it reaches the earth. •For this work, we assume that suspended raindrops are perfectly spherical. Picture (7). Rainbow Formation There are three optical processes occurring in the diagram above: •Refraction •Total Internal Reflection •Dispersion • Refraction Snell’s Law: θ1 n1 n2 θ2 • Total Internal Reflection (TIR) Light that is refracted into the drop also hits the back of the drop. The critical angle for TIR is: Any light hitting the inside of the drop above this angle will be reflected internally. • Dispersion Light of different wavelengths sees a different index of refraction inside a given media. The dispersion processes that occur in rainbows fall in the normal dispersion regime, so as wavelength decreases, the index of refraction will increase. For water (1): Color Red Yellow Blue This effect is easily seen in prisms. Picture (4). Wavelength 650 nm 580 nm 475 nm Index 1.331 1.333 1.340 Consequences of Rainbow Physics • All rainbows are formed on a line that connects the sun, the viewer, and the center of the rainbow. • Rainbows form best shortly after sunrise and before sunset, though ample light must be present. • Rainbows are a direct result of Fermat’s Principle: Light will take the path of shortest time from the source to the point of observation. Multiple Rainbows Rainbows Some light incident on a raindrop will be doubly internally reflected as shown below. This leads to a double rainbow. Picture (3). Multiple Rainbows Rainbows This figure explains why Homer sees the second rainbow inverted as compared to the first. The secondary rainbow will be fainter than the first because some light is lost upon the second internal reflection. 54.5º 52º 42º 40º Circular rainbows are a direct result of the same processes that make regular rainbows. Normally, the ground cuts off a portion of the rainbow. As seen from an airplane, the planes shadow will always be in the center of the rainbow. Picture (2). 42º Reflection Rainbows Rainbows can also be formed by light reflected off a surface, such as water. This reflected rainbow is not as bright as the original since not all light is reflected. Reflected Rainbow Primary Rainbow Why is the sky dark between rainbows? Dark Region Bright Region Lots of light is scattered from the raindrops at angles below the rainbow ray angle, but little above it. Consequently, the sky inside the rainbow will be brighter than that outside. Secondary rainbows exhibit the opposite phenomena, so their bright region is above them. Supernumerary Arcs The above picture clearly shows several faint arcs of light below the primary rainbow. These are known as supernumerary arcs. These arcs result from the interference of light from the same drop. Picture (5). Supernumerary Arcs Interference of waves exiting a single drop create supernumerary arcs. Recall that when seen by the viewer, the supernumerary arcs will appear below the main rainbow. Picture (6). Interesting Rainbow Facts • The distance to a rainbow depends on the distance between the observer and the droplets. A rainbow made with a garden hose is often within reach. • No two people will ever see the same rainbow. As a matter of fact, each eye sees a slightly different rainbow. • The myth that there is a pot of gold at the rainbows end originated in old Europe. Many cultures have come up with interesting ways of explaining rainbows and their mythical powers. Conclusions • Rainbows are a naturally occurring side effect of Fermat’s principle. • Different types of rainbows are formed for different geometrical situations. • Rainbows and Liquid Crystals??? I know Dr. Palffy has looked into them, but could they actually work? What new properties would they exhibit? A switchable rainbow? Elliptical rainbows? References 1. 2. 3. 4. 5. 6. 7. Muller, R.; Slow Light; http://muller.lbl.gov/teaching/Physics10/chapters/13Slow_Light.html (2001). Tilden, B.; http://www.bobtilden.com/1B02.htm Mikolaj; Sawicki, P.; http://www.jal.cc.il.us/~mikolajsawicki/rainbows.htm No photographer listed; www.exploratorium.edu/imagery/ stills/Prism.jpg Fraser, A.; http://www.usna.edu/Users/oceano/raylee/RainbowBridge/Chapte r_8.html Lee, R.; http://www.usna.edu/Users/oceano/raylee/RainbowBridge/Chapte r_8.html Townsend, G.; http://www.cs.arizona.edu/camera/album/jpg/rainbow.jpg