Refraction

=**Refraction**=


 * Refraction** is the bending of light as it passes one substance to another. The speed changes when the light passes through the first substance (medium) to the next. The differences in density, or the refraction index, cause the bending of light according to the angle of incidence between the light and the horizontal normal line when leaving the initial medium. When entering the next medium, the angle is then called the angle of refraction.

toc =History= Greek astronomer Ptolemy studied refraction in the 2nd century. Ptolemy worked out a law of refraction, which is only accurate for small angles. In the 10th century, Arabian optical engineer and mathematician, Ibn Sahl, also worked out a law of refraction. The law was rediscovered in 1602 by the British astronomer and mathematician Thomas Harriot. However, due to his lack of confidence in his discoveries, Harriot never showed his work to the public. The law was again discovered by Willebrord Snell in 1621, but Snell died in 1626 before sharing his results.

=Snell's Law= Willebrord Snell derived a formula for determining the relationship between the angle of incidence and the angle of refraction as it passes from one medium to another:


 * n subscript 1 represents the initial medium
 * sine beta subscript 1 represents the angle of incidence
 * n subscript 2 represents the second medium
 * sine beta subscript 2 represents the angle of refraction

Ex. 1
For example, if the medium of air is 1.00 (n sub 1), the medium of water is 1.33 (n sub 2), and the angle of incidence is 45 degrees (sin beta sub 1). We find the angle of refraction by using the equation. //(Answer at the bottom)//

Ex. 2
Another example would be finding the second medium with ice (1.31) as the initial medium, the angle of incidence at 30 degrees, and the angle of refraction at 20 degrees. By finding the index of refraction for the second medium, you can go to the list of indexes and find the corresponding material. (//Answer at the bottom)//

Ex. 3
In this example, the index of the first medium will be 1.02, the angle of incidence will be 50 degrees, and the index for the second medium will be 1.89. //(Answer at the bottom)//

= **Speed of Light in a Medium (Index of Refraction)** = The speed of light (c= 3 *10^8 m/sec) in a vacuum is one of the most common constants when dealing with optics. However, the speed of light is slowed down when entering a medium. The index of refraction of the medium is described with an equation: 

Ex. 4
Using this formula, we are able to find the index of refraction to a medium. For example, if the velocity of the light is 5.8*10^8 m/s, we find the index of refraction by dividing the speed of light by the velocity. //(Answer at the bottom)//

Ex. 5
We can also use this formula to find the velocity of light when the index is 1.87. //(Answer at the bottom)//

Ex. 6
Now we'll find the velocity of the light when the index is 1.02. //(Answer at the bottom)//

=The Rainbow= When light passes through a prism, different colors of the light refract at different angles. They disperse and become individual colors that are visible to the human eye.



The colors are arranged by wavelength (longest to shortest):
 * Radio wave
 * Microwave
 * Infrared
 * Red
 * Orange
 * Yellow
 * Green
 * Blue
 * Violet
 * Ultraviolet
 * X-Ray
 * Gamma Ray

=List of Refraction Indexes=
 * Material || Index ||  ||
 * Vacuum || 1.00000 ||
 * Air at STP || 1.00029 ||
 * Ice || 1.31 ||
 * Water at 20 C || 1.33 ||
 * Acetone || 1.36 ||
 * Ethyl alcohol || 1.36 ||
 * Sugar solution(30%) || 1.38 ||
 * Fluorite || 1.433 ||
 * Fused quartz || 1.46 ||
 * Glycerine || 1.473 ||
 * Sugar solution (80%) || 1.49 ||
 * Typical crown glass || 1.52 ||
 * Crown glasses || 1.52-1.62 ||
 * Spectacle crown, C-1 || 1.523 ||
 * Sodium chloride || 1.54 ||
 * Polystyrene || 1.55-1.59 ||
 * Carbon disulfide || 1.63 ||
 * Flint glasses || 1.57-1.75 ||
 * Heavy flint glass || 1.65 ||
 * Extra dense flint, EDF-3 || 1.7200 ||
 * Methylene iodide || 1.74 ||
 * Sapphire || 1.77 ||
 * Rare earth flint || 1.7-1.84 ||
 * Lanthanum flint || 1.82-1.98 ||
 * Arsenic trisulfide glass || 2.04 ||
 * Diamond || 2.417 ||

=Answers= Example 1: //n(1)sin(1)=n(2)sin(2)//

//(1.00)sin(45)=(1.33)sin(2)//

//sin(45)/1.33=sin(2)//

//sin(2)=32.12 degrees//

Where:
 * n(1) is the initial medium
 * sin(1) is the angle of incidence
 * n(2) is the second medium
 * sin(2) is the angle of refraction

Example 2//:// //n(1)sin(1)=n(2)sin(2)//

//(1.31)sin(30)=n(2)sin(20)//

//0.655/sin(20)=n(2)//

//n(2)=1.92//

Where:
 * n(1) is the initial medium
 * sin(1) is the angle of incidence
 * n(2) is the second medium
 * sin(2) is the angle of refraction

Example 3: //n(1)sin(1)=n(2)sin(2)//

//(1.02)sin(50)=(1.89)sin(2)//

//0.781/1.89=sin(2)//

//sin(2)=24.41 degrees//

Where:
 * n(1) is the initial medium
 * sin(1) is the angle of incidence
 * n(2) is the second medium
 * sin(2) is the angle of refraction

Example 4: //n=c/v//

//n=(3*10^8 m/s)/(2.1*10^8 m/s)//

//n=1.43//

Example 5: //n=c/v//

//1.87=(3*10^8 m/s)/v//

//(3*10^8 m/s)/1.87=v//

//v=1.6*10^8 m/s//

Example 6: //n=c/v//

//1.02=(3*10^8 m/s)/v//

//(3*10^8 m/s)/1.02=v//

//v=2.94*10^8 m/s//

**References** http://interactagram.com/physics/optics/refraction/ http://amazing-space.stsci.edu/resources/explorations/groundup/lesson/glossary/term-full.php?t=refraction http://suite101.com/article/refraction-of-light-a50691  http://hyperphysics.phy-astr.gsu.edu/hbase/tables/indrf.html  []