Light Phenomena: Reflection, Refraction, Dispersion

Updated 2012Aug16

Dr. Bill Pezzaglia

Light & Optics

OutlineA. The Law of Reflection

1. Reflection Law of Euclid2. Principle of Least Distance3. Images in a Mirror

B. The Law of Refraction1. Fermat’s principle, Snell’s Law2. Critical angle, total reflection3. Refractive images

C. Dispersion of Light1. Prism disperses colors2. Newton’s experiments3. Sellmeier equation

D. References

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A. Reflection

1. The law of reflection

2. Principle of “least distance”

3. Image in a plane mirror

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A. Law of Reflection 4

1. Mirror and Virtual Images

(a) The Law of Reflection (Euclid 300 BC)

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2. Principle of Least Distance

• Heron of AlexandriaLight follows path of least distance(e.g. when reflecting off of water)

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

3. Mirror and Virtual Images7

“image” you

“real” you

mirror onlyneeds to be half as

high as you are tall. Yourimage will be twice as far from you

as the mirror.

B. Refraction

1. Fermat’s Principle of Least Time & Snell’s law (1621)

2. Total Reflection (Snell’s window)

3. Refractive Images

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1. Fermat’s 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 Snell’s Law This is the path light (sound, any wave) will take!

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Lifeguard Tower

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11

sin1

sin1

vv

1b. Snell’s Law (1621) 10

2211 sinsin nn

Path of wave is bent toward normal when enters media with lower wavespeed (i.e. higher index of refraction)

2a. Total Reflection (Snell’s Window)

• At the “critical angle” the refracted beam is at 90, so it can’t get out.

• Greater than this “critical angle” there is 100% reflection

• Snell’s Window: from underwater a fish sees the entire area above surface in a cone. Outside the cone light is totally reflected

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2b. Total Reflection

• Total 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.

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425.1

1arcsin

arcsin

90sinsin

1

2

221

c

c

c

n

n

nnn

3. Refraction and Images

• The bottom of a river will appear to be shallower than it really is. Why?

• The apparent depth:

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n

dd '

C. Dispersion

1. Phenomena

2. Newton’s Experiments

3. Sellmeier Equation

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1. Dispersion of a Prism

Early theories were that a prism created color. White light goes in, colors come out.

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2a. The Components of Light13

1672 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 Light14

1672 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 Media• In 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 workwas doneby Newton

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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)

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2

0

20

1

11)(

nn

References

• http://www.thestargarden.co.uk/RefractionReflectionDiffraction.html

• http://www.olympusmicro.com/primer/lightandcolor/reflectionintro.html

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