In the early 1600’s a Dutch scientist named Willebrord Snell studied the behavior of light as it passed through media such as water and glass. He carefully plotted the paths of light rays and measured angles of incidence and refraction. Through trial and error he looked for a relationship between the angles. After many trials (and errors) he found the following relationship:

In other words, he found a direct relationship between the sine of the angle of incidence and the sine of the angle of refraction. He found the constant to be:  

• constant for a given medium, even after repeated trials This implies that the constant is a characteristic property of the medium (such as water), and so can be used to identify the  substance  
  
  Independent of the angle of incidence  

The constant was given a name, the index of refraction, and is represented by n. Snell never publicized his work. The relationship was published by Rene Descartes in 1637, and is known as Snell’s Law:

The relationship above holds for a light that travels from air into a more optically dense medium such as water.  

ex.        A ray of light is incident on a piece of glass at an angle of 30^o with the normal. The angle of refraction is measured to be 18^o. Calculate the index of refraction.

ex.        A ray of light is incident on the same glass as in the previous example, but this time at an angle of 40^o. Calculate the angle of refraction.   

Because the glass is the same, the index of refraction is 1.62.

Try-It-Yourself: 

1. >    A ray of light is incident on plexiglass at an angle of 50o. The angle of refraction is 33o.