Snell's Law.



Some Background on Snell's Law:

This form of Snell's law was actually published by Descartes as the Law of Sines. Snell did discover the relationship but articulated it in a different way. Today the form used by Descartes is what is known as Snell's law.

The law is described by the formula:
 

If the top part of the diagram is air, n1 is the index of refraction of air, and if the bottom part is glass, n2 is the index of refraction of glass.

Snell and Descartes realized that when light went from one medium to another, the angles and refractive indices of the media determined the path that the light followed. The relationship is a function of the sine of the angles.

Refraction

When we refer to the velocity of light, what we're usually talking about is the velocity of light in a vacuum, which is 3.00 x 10^8 m/s. When light travels through a material, such as glass, diamond, or plastic, it travels at a slower velocity. The index of refraction of a medium that transmits electromagnetic waves is the ratio of the velocity of propagation of an electromagnetic wave in a vacuum to the velocity of propagation of the wave through the medium.

An index of refraction can be computed by using the formula  n = c / v, where n is the index of refraction of the medium, c is the velocity of light in a vacuum, and v is the velocity of light in the medium.

The change in velocity that occurs when light passes from one medium to another is responsible for the bending of light, or refraction, that takes place at an interface. If light is travelling from medium 1 into medium 2, and angles are measured from the normal to the interface, the angle of transmission of the light into the second medium is related to the angle of incidence by Snell's law :

 

How to Use this Applet:

The applet is divided into two parts, a control panel and an action panel.  The control panel has tools you can use to explore the Snell's law. Our representation of Snell's law goes a little further than exploring only electromagnetic waves.  We represent two types of seismic waves that travel through the earth after an earthquake occurs: primary and secondary, which are really like sound waves rather than light.
You can choose which one is the incident waves.
    Each incident wave can produce up to 4 waves:

P1 -- velocity of primary wave in medium 1
P2 -- velocity of primary wave in medium 2
S1 -- velocity of secondary wave in medium 1
S2 -- velocity of secondary wave in medium 2

Incident Angle, Primary Refracted Angle, Secondary Refracted Angle, Primary Reflected Angle and Secondary Reflected Angle are self-explanatory.

NOTE: information can be entered in any field and it will updated on the action screen.

Action Panel: relects all the changes made in the Control Panel, also is interactive: you can change the incident angle just by dragging the cursors in the white area. All the changes are shown in the Control Panel.

Critical Angle: The critical angle can be found from Snell's law, putting in an angle of 90 for the angle of the refracted ray. This gives:
 

For any angle of incidence larger than the critical angle, Snell's Law will not be able to be solved for the angle of refraction, because it will show that the refracted angle has a sine larger than 1, which is not possible. In that case all the light is totally reflected off the interface, obeying the law of reflection.

3 out of 4 produced waves may reach critical angle (refracted anlge of incident wave has the same angle as incident angle)
 


Source code files:

Bytecode files:

Snell.java

Snell.class

DrawPanel.java 

DrawPanel.class 

ButtonHandler.java 

ButtonHandler.class 

SeismicWaves.java

SeismicWaves.class 

PolarCoordinateSystem.java

PolarCoordinateSystem.class

ColorPanel.java

ColorPanel.class

MyListener.java

MyListener.class

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