# Reflection and Refraction of Electromagnetic Waves

• Light waves are one variety of electromagnetic waves
• E-M waves are transverse
• E-M waves cover a vast span of wavelength and energy
• Physicists measure angles of light rays relative to the normal to a surface
• When light waves reflect from a smooth surface, the angle of reflection equals the angle of incidence
• When light moves from one medium to another, it
• changes wavelength
• changes speed
• changes direction
• The ratio of the speed of light in a vacuum to its speed in some medium is the index of refraction of that substance
• The wavelength of light in a medium is equal to its wavelength in a vacuum, divided by the index of refraction of the medium
• If a light ray hits a boundary between two media at some angle theta1 to the normal, it is refracted into the second medium at an angle theta2 given by Snell's Law:
```                 n1 * sin(theta1) = n2 * sin(theta2)
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Another way to show the huge span of the electromagnetic spectrum is to compare it to ... a piano.

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Joe (in Rochester) calls his friend Phillipe, who lives in Paris. As they talk, Joe notices something wierd -- there's always a short pause before Phillipe answers his questions.

"Are you playing some stupid video game?" he asks in an irritated tone of voice.

"Non," replies Phillipe after a pause of 0.48 seconds, "these delays are due simply to the speed of light."

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Q:  What does Phillipe mean?

Q:  Roughly how far above the surface of
the Earth are communications satellites?

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There is a relatively simple relationship between the angle of the incident ray measured from the normal and the angle of the refracted ray measured from the normal.

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Joe can move his laser pointer anywhere along
a horizontal line 12 cm above the water's surface.
He wants to strike the water at the point A,
and have the beam hit the "X" at the bottom of the tank.

How far along the green line from point A should
Joe put his laser pointer?

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Consider a prism of plastic in the form of
an equilaterial triangle, with index of
refraction n2 = 1.30.  An incoming
ray of blue light strikes the left face
of the prism at angle theta1 = 30 degrees.

Q:  What is the angle theta2?

Q:  Angle theta3 = 60 - theta2.
Can you figure out angle theta4?

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Q:  What angle should yield total internal
reflection for a laser beam passing
FROM water INTO air?

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