Illuminating Math with Optics, funded by SPIE, the international society for optics and photonics
Magic, Refraction and Trig
First the magic:
Get two small paper cups and fill one with water. Place the penny at the bottom of one cup,
near the side.
Move the cup along the table until you can no longer see the penny.
While not changing your point of view (don't move your head!) very slowly pour water into the
cup. Be careful not to move the penny with the water stream. What happens?
Magic! You can now see the missing penny!
Not so fast- it's not magic, it's physics! Specifically, it's REFRACTION
When waves change speed their wavelength and direction of travel change too.
High speed
Long wavelength
n1
θ1
It's simpler to just
look at the wave
direction
Low speed
Short wavelength
θ2
n2
"n" is the index of refraction. It indicates how fast the wave is traveling. The larger the value of
n, the slower the wave is traveling.
And now the trig...
If you know the index of refraction of the material the wave is traveling in you can predict how
a wave will bend from Snell's Law:
n1 sinq1 = n2 sinq 2
Illuminating Math with Optics, funded by SPIE, the international society for optics and photonics
Explaining the penny trick
Light acts like a wave when it travels from water into air. Which way does light bend? (Snell's
law also explains how lenses work, like the lens you'll use in the matrix experiment.)
The glass is empty
and light from the
penny reaches my
eye. I see it.
I moved the empty
glass and light
doesn't reach my
eye. I can't see it.
What happens
when the glass is
full? Where does
the light go?
??
YOU DO THE MATH
1. At what angle does light leave the water (θ1)? The cup is 6 cm high and the penny is 4 cm
from the vertical axis.
6 cm
θ1
4 cm
2. The index of refraction for water (n2) is 1.33 and the index of refraction for air is about 1.0
(n1). Use Snell's law to find the angle light make with the axis in air. Draw a diagram to explain
why you can now see the penny.
.................To scoop a fish from a tank, do you put the net above or below the fish?...............