To a physicist, light could be defined as a “transverse wave that travels in straight lines, called rectilinear propagation”. Your local Random House Dictionary Representative would likely say that light is “that which makes things visible or affords illumination”. In any case, light is, simply put, what lets us see. When we see an object, light reaches our eyes from different points on the object. The light leaving the object travels in many different directions but only a small bundle reaches our eyes.

The Speed of Light

Light is fast, very fast. Faster than you can run, even if you are feeling particularly fast that day. Faster than a car. Really fast. In a vacuum, it travels at 300 000 kilometers per second. In relative terms, it would take a very small amount of time to travel from Tokyo, Japan to Winnipeg, Canada. The speed of light is represented by C, where C= 3 * 108 m/s. The speed of light was not known for several thousand years. Due to this, it was also not known if light had a finite or infinite speed. In 1500 AD, Galileo attempted to calculate the speed of light. In his experiment , Galileo flashed a beam of light to his friend with a mirror on a nearby hill, and his friend flashed him back....with a mirror. Through this experiment, Galileo tried to measure the time it took for the light to travel to the nearby hill and back. He concluded that “if not instantaneous, then it is extraordinarily rapid.” That may not seem like a stroke of genius to us, but im sure Galileo was proud of himself. In 1675, Olaus Roemer found that the period of IO, a moon of Jupiter, was longest when the Earth was farthest away from Jupiter. From this Roemer showed that light had a finite speed. v=d/t = 3 * 1011m/ 1320 seconds = 2.3 *108m/s, this turned out to be a fairly accurate measurement.

It was not until the 1920's with Albert A. Michelson and an eight-sided mirror, which is called "The Michelson Mirror" (how original), that the currently accepted speed of light was found.

Refraction can be defined as the bending of a wave when it enters a new medium. For example, if light is moving through the air, and then it enters some water, it has changed its medium. And you thought medium was just the size of your underwear. Well its not. In wave equations, we often draw a line called the "normal." The “normal” is a line drawn perpendicular to the boundary between the two mediums. If you stood on the boundary between two mediums, with your medium underwear on, and if you were at exactly 90 degrees, would you be normal? Not likely. The normal is just a pretend line that we use as a reference.

Light only refracts when it enters a medium at any angle other than 90. In the diagram below, there is no refraction.

If light hits the boundary at any angle other than 90 degrees, the angle it makes with the normal is called the angle of incidence (angle i). Then, after passing through the boundary, the angle it makes with the normal is called the angle of refraction (angle r). When light travels from a slow medium to a fast medium, it bends away from the normal. When light travels from a fast medium to a slow medium, it bends towards the normal.

The index of refraction can be calculated in a variety of ways. Primarily, the formula:

n = C / v
is used. C represents the speed of light in a vacuum, v represents the speed of light in the material, and n stands for the index of refraction. However, the index of refraction can be calculated in a number of other ways as well. There is never a shortage of formulas in physics!

The other formulas are:

n = v1/v2

“v1“ is the speed of light in the first medium

“v2“ is the speed of light in the second medium

n = sin i/sin R

“sin i” is the sin of the angle of incidence

“sin R” is the sin of the angle of refraction

n = wavelength_1 / wavelength_2

As well, the formula n2/n1 can be used in equations in conjunction with any of the above formulas. In other words,

n2/n1 = v1/v2 = sin i/sin R = wavelength_1/wavelength_2

In that equation, ‘n1' would be equal to the index of refraction in the original material, while ‘n2' would be equal to the index of refraction in the second material.

When a light ray enters a new medium, refraction does occur. However, not all of the ray refracts, some reflects back into the original medium. We can relate the two laws of reflection to this:

The Angle of Incidence (angle i) is equal to the Angle of Reflection (angle rf).
The Incident Ray, the Normal Ray and the Reflected Ray all lie in the same plane.

(You shouldn't have to worry about the 2nd law so long as we are thinking in 2 dimensions.) So just remember- the angle of reflection is the same as the angle of incidence. And don't get Reflection confused with Refraction!

Snell. Interesting name there, kind of fun to say. Snell Snell Snell. If your name is Snell, we hope we haven't offended you. Actually, there was a famous scientist named Snell. Snell’s Law can be used to find either the angles of incidence or refraction or either of the indexes of refraction in a refraction problem. To understand Snell’s Law, we should derive it! How? Well, in this case, we'll teach by example.

Lets say, just for fun, a light ray decides to travel from glass into water. Pretend its going on vacation or something. We know that the index of refraction for a substance can be calculated using n = C/v, and by watching this cool algebra and formula manipulation, one can actually derive Snell’s Law.

Glass

n = C/v
v * n = C

Water

n = C/v
v * n = C

At this step, we discover that these two equal each other. Therefore:

v(glass) * n(glass) = v(water) * n(water)
v(glass)/v(water) = n(water)/n(glass)
v1/v2 = n2/n1

But we know that v1/v2 = sin i/ sin R so...

sin i/ sin R= n2/n1
n1 * sin i = n2 sin R

Which is equivalent to Snell’s Law:

n1 * sin angle 1 = n2 * sin angle 2

Example Problem

A ray of light enters a pool of Ethyl Alcohol (n = 1.36), from air (n = 1.0003), with an angle of incidence of 30°. What is the angle of refraction of the light in the Ethyl Alcohol?

Given:

Angle of Incidence = 30°

Ethyl Alcohol - n = 1.36 <--------n2

Air - n = 1.0003 <--------n1

Formula:

n1 * sin 1 = n2 * sin 2
Work:

(1.0003) * sin(30°) = (1.36) * sin R

(1.0003) * sin(30°) / (1.36) = sin R

21.58° = Angle of Refraction

Answer:

The Angle of Refraction in the Ethyl Alcohol is 21.58°.