The Math of Refraction

Snell's Law states: 

ni = the index of refraction of the incident medium (in my case, the air)
nr = the index of refraction of the refraction medium (in my case, the canola oil)
(θi) = angle of incidence (in air)
(θr) = angle of refraction (in canola oil)

In the pictures I took of the glow stick in water and canola oil, this formula can help me find the index of refraction for each substance. The index of refraction is equal to the speed of light in a vacuum (a volume of space with empty matter) divided by the speed of light in the medium. I picked a photo and placed a protractor on it to measure the angles.



The angle of incidence is the angle that the glow stick is sitting in the glass cup and how we see it in the air.

The angle of refraction is the angle at which the glow stick is sitting in the canola oil in the glass and how we see that because of the speed of light.

I know that the index of refraction in air is about 1.0003. The angle of incidence is 29 degrees. The angle of refraction is 37 degrees. Now I can plug these numbers into the equation to find the index of refraction of canola oil.

1.0003 * sin(29) = nr * sin(21)

1.353 = nr 

So the index of refraction of the canola oil is 1.353

Then I can take this and plug it into the equation for index of refraction.

index of refraction = (speed of light in vacuum)/(speed of light in medium)

1.353 = (299792458 m/s)/(speed of light in canola oil)

(299792458 m/s)/(1.353)=speed of light in canola oil

speed of light in canola oil = 221,576,000 m/s


When LIGHT goes from one medium to another, it will bend. When it goes from less dense to more dense, it bends towards. When it goes from more dense to less dense, it bends away. Because I am using a glow stick, which is not light, it is doing the opposite. So The angle is 37 degrees away. That is 8 degrees more than 29 degrees where it originally was. Therefore, I need to subtract 8 from 29 to get 21 degrees. 21 degrees is the angle I will use for the angle of refraction.