Clicker Question - UMD Physics · 2006-02-08 · 1 1 William Wegman 2 a b c d e P parking lot Q Clicker Question loose sand A group of sprinters gather at point P on a parking lot

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William Wegman

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a b c d e

parking lotP

Q

Clicker Question

loose sand

A group of sprinters gather at point P on a parking lotbordering a beach. They must run across the parking lotto a point Q on the beach as quickly as possible.Which path from P to Q wins? You should consider therelative speeds of the sprinters on the hard surface of theparking lot and on loose sand.

1. a)2. b)3. c)4. d)5. e)6. they all take the same time

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Fermat’s Principle

Light travels in the path that takesthe least amount of time.

P Q

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• Remember that when the light goes from adense (large n) to a less dense medium(small n), the angle of transmission islarger….

• From water to air, if the incident angle is~50o, the transmitted angle ~ 90o. If theincident angle is larger, there is NOtransmission at all!

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Incoming Reflection

Refraction_r

http://www.phy.ntnu.edu.tw/java/light/flashLight.html

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• The incident angle at which the totalinternal reflection just occurs is calledthe critical angle.– From glass to air, 42°– From water to air, 50°– From diamond to air, 24. 5°

Critical Angle

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Fiber Optics

• Use thin, flexible glass or plastic fibersas light pipes

• If the light hits the surface at an anglelarger than the critical angle, it is totallyinternally reflected: No loss of light!Thus the light can be used to transmitinformation through the optical fibers.

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• Why is the fiber optical transmission isbetter?– Light has high frequency of oscillation:

send much more information!– All phone calls to Europe/Asia go by fiber– All main internet lines (backbone) are fiber– Look for “fiber to the home”

• Other uses:– See and photograph theinside of vital organs (endoscopy)

Fiber Optics

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What is a mirage?

•The index of refraction of the air is not quite equal to 1,and it changes with temperature.• A continuous change of the index of refraction makesa light bend from its original direction.• A hot, dark asphalt road can cause the light to bend,producing a mirage. 10

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Dispersion

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Newton’s Discovery• Newton (at the age of 23) reached

the revolutionary conclusion thatwhite light is not a simple,homogenous entity, as naturalphilosophers since Aristotle hadbelieved.

• When he passed a thin beam ofsunlight through a glass prism, henoted the oblong spectrum of colors:red, yellow, green, blue,violet– thatformed on the wall opposite.

Sir Isaac Newton, age 47

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Dispersion

• The index of refraction is frequency-dependent.

water glass diamondRed λ=656 nm 1.331 1.571 2.410

Yellow λ=589 nm 1.333 1.575 2.418

Blue λ=434 nm 1.340 1.594 2.450

• Snell’s Law => different colors refract by differentangles

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Dispersing Prism

Since nblue > nred, blue is bent to greater angle

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Optical properties ofdiamond

• Diamonds has a large index of refraction(n=2.4) and a small critical angle 24.5°.

• The diamond surfaces are cut so thatmost of light entering a diamond iseventually reflected back out the front ⇒brilliance!brilliance!– if you look from the back, the diamond is black.

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The right cut

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Rainbows

• Because of the dispersion of water,droplets of water can break up the sunlight into a spectrum ⇒ rainbow

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42°

Dispersion in a droplet

refractionreflection

refraction

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All rays from a rainbow comefrom different raindrops.

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The Arc of a rainbow

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Double Rainbows

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Double Rainbows

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refraction

reflection

reflectionrefraction

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Halos and Sun DogsHalo

Sun dogs

Refraction in ice