# Light Phenomena: Reflection, Refraction, Dispersion Updated 2012Aug16 Dr. Bill Pezzaglia Light & Optics

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• Light Phenomena: Reflection, Refraction, Dispersion

Updated 2012Aug16

Dr. Bill Pezzaglia

Light & Optics

• OutlineThe Law of ReflectionReflection Law of EuclidPrinciple of Least DistanceImages in a MirrorThe Law of RefractionFermats principle, Snells LawCritical angle, total reflectionRefractive imagesDispersion of LightPrism disperses colorsNewtons experimentsSellmeier equationReferences

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• A. ReflectionThe law of reflection Principle of least distance Image in a plane mirror*

• A. Law of Reflection *

• 1. Mirror and Virtual Images(a) The Law of Reflection (Euclid 300 BC)*

• 2. Principle of Least DistanceHeron of Alexandria Light follows path of least distance (e.g. when reflecting off of water)

*Which path should an ant take to get to the opposite end of the box fastest?

• 3. Mirror and Virtual Images*mirror onlyneeds to be half ashigh as you are tall. Yourimage will be twice as far from youas the mirror.

• B. Refraction Fermats Principle of Least Time & Snells law (1621) Total Reflection (Snells window) Refractive Images*

• 1. Fermats Principle Lifeguard Dilemma: What is the fastest path to drowning man? Note you can run twice as fast as you can swim. Run straight to river, then swim Run further to shore adjacent swimmer then swim Optimal path obeys Snells Law This is the path light (sound, any wave) will take!*Lifeguard Tower

• 1b. Snells Law (1621) *Path of wave is bent toward normal when enters media with lower wavespeed (i.e. higher index of refraction)

• 2a. Total Reflection (Snells Window) At the critical angle the refracted beam is at 90, so it cant get out. Greater than this critical angle there is 100% reflection Snells Window: from underwater a fish sees the entire area above surface in a cone. Outside the cone light is totally reflected *

• 2b. Total ReflectionTotal reflection will only occur if going from dense media to less dense! For glass (n=1.5) the critical angle is 42 Optical fibers are designed so the light is always 100% reflected, and bounces down the fiber.*

• 3. Refraction and Images The bottom of a river will appear to be shallower than it really is. Why? The apparent depth:*

• C. Dispersion Phenomena Newtons Experiments Sellmeier Equation*

• 1. Dispersion of a PrismEarly theories were that a prism created color. White light goes in, colors come out.12

• 2a. The Components of Light131672 Newton shows that the prism does not create color, it merely separates (disperses) the colors in the white light

The second prism does not create more colors.

• 2b. The Components of Light141672 Newton further shows that a second prism can recombine colors to make white light. Hence white light is a mixture of all colors.

• 3a. Speed in MediaIn media (such as glass) the speed is slower. This causes refraction the bending of light.The speed usually depends upon the wavelength, called dispersion. This causes the colors to be spread out.

This work was done by Newton

23

• 3b. Sellmeier Equation (1871) In media the speed of light depends upon wavelength (color) Sellmeier Equation (1871) shows index of refraction decreases for bigger wavelength, approaching n0 Index of refraction goes to infinity at color 0 of media (e.g. green for emerald)*

• Referenceshttp://www.thestargarden.co.uk/RefractionReflectionDiffraction.html http://www.olympusmicro.com/primer/lightandcolor/reflectionintro.html *

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