AY80B Lecture 7

Astronomy 80 B: Light Lecture 7: Refraction, dispersion, rainbows 22 April 2003 Jerry Nelson Topics for Today • Optical illusion • Review of Quiz – Statistics – Solutions • Total internal reflection • Mirages • Index of refraction of materials • Dispersion (and a green flash) • Rainbows • Sundogs 2003• AprilHalos 22 80B-Light 2 AY 80B Quiz 1 results 20 80 18 distribution of scores 70 integrated number 16 60 14 average = 59 50 12 10 40 # of students 8 30 cumulative number 6 20 4 10 2 0 0 0 102030405060708090100 score (out of 90) 2003 April 22 80B-Light 3 Derivation of Snell’s law from wavefront continuity θ i n=c/v A’ 1 n1 θ i B’ A θ t Time for light to go from A’ to B’ 2 n2 B ==d AB'' =n1 θ tAB'' AB' sin i v11cn/ c d AB n t == =2 AB' sinθ θ AB' t t v22cn/ c so = ttAB'' AB θθ= Which yields nn12sinit sin Refraction and Total Internal Reflection • When light travels from a higher index of refraction material to a lower one, total internal reflection is possible 2003 April 22 80B-Light 5 2003 April 22 80B-Light 6 Application of total internal reflection • Binoculars use prisms and total internal reflection to erect the image and shorten the size 2003 April 22 80B-Light 7 Fiber Optics • Fiber optics employ total internal reflection to transmit light with negligible losses over large distances and (with bundles) to transmit images 2003 April 22 80B-Light 8 Refraction through multiple parallel layers ( atmosphere) θ n 1 nnsinθθ= sin 1 1122 θ n 2θ θθ= 2 2 nn2233sin sin θ θ θθ= n3 3 3 nn3344sin sin θ θ • n4 4 4 • n5 • so So, the final angle only depends on the nnsinθθ= sin initial angle and index of refraction and the 11. kkfinal index of refraction, not on the intermediate indices 2003 April 22 80B-Light 9 Refraction Gradients bend light • When the index of refraction changes gradually, light bends, moving towards the higher index region 2003 April 22 80B-Light 10 2003 April 22 80B-Light 11 Mirage on a hot road 2003 April 22 80B-Light 12 • Index variations can cause unusual and beautiful effects 2003 April 22 80B-Light 13 Dispersion • Dispersion in glass, along with a prism geometry, produces colors from a white light source 2003 April 22 80B-Light 14 Prisms and color • A prism separates white light into its constituent colors • These colors cannot be separated any more • These colors can be recombined into “white” light 2003 April 22 80B-Light 16 Common Indices of Refraction • Material Index – Vacuum 1.0 – Air 1.0003 – Ice 1.31 – Water 1.33 – Alcohol (ethyl) 1.37 – Plastics ~ 1.5 – Glass 1.5 – Cubic Zirconia 2.15 – Diamond 2.4 2003 April 22 80B-Light 17.

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CUBIC ZIRCONIA: an UPDATE by Kurt Nassau
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