The Speed of Light
You may have learned that the speed of light is constant (about 30 000 000 metres per second). In actual fact it is only constant if it is travelling through a medium (material - eg. air) of constant density. When light encounters an increase in density, it slows down. When light encounters a decrease in density it speeds up. These changes in speed correspond to changes in direction so changes in density cause the path of light to bend. See below. ## Air to Water

When light travels from air to water it slows down because water is more dense than air is. When light slows down its path bends towards the normal line so that the angle of incidence (i) is greater than the angle of refraction (r),   i  > r.   Eg.  As light travels from air to water it is  bent towards the normal line, i.e. the  angle of incidence is greater than the  angle of refraction. This also occurs in the formation of a rainbow. The normal line it perpendicualr to the tangent at the point where the light hits the surface of the raindrop.

## Water to Air

When light travels from air to water it slows down because water is more dense than air is. When light slows down its path bends towards the normal line so that the angle of incidence (i) is greater than the angle of refraction (r),   i  > r.   Eg.  As light travels from air to water it is  bent towards the normal line, i.e. the  angle of incidence is less than the  angle of refraction. When light travels back out of the raindrop, the same thing occurs. The diagram above shows the angles for  the violet ray.

## Refractive Index

It is possible to find the angles of incidence refraction by careful ray-tracing and measurement. You may have tried this using a Hudson Light Box. This method is time consuming and can be very inaccurate. For this reason scientists in the 16th and 17th centuries devoted years to trying to find a mathematical relationship to link the values of the angle of incidence and the angle of refraction.

In 1621 Willebrord Snell, a Dutchman, found that when the sin of the angle of incidence is divided by the sin of the angle of refraction, the result is a constant value for a given interface (boundary layer between specific materials). This constant number was named the Relative Refractive Index and is specific for each pair of media. For an air-to-water interface, the relative refractive index is 1.33.

A more useful quantity is the Absolute Refractive Index. This is the relatve refractive index for a vacuum-to-medium interface and is specific for each medium. Some examples are:  Rock salt = 1.54,  Diamond = 2.42,  Ethyl Alcohol = 1.36.
(Figures quoted from Eddy De Jong, 1991. Physics One, Heinemannn Australia.)

## Snell's Law

The relationship between the angles of incidence and refraction is now known universally (except in France ) as Snell's Law. See below. Where: i   is the angle of incidence  r   is the angle of refraction  n* is the relative refractive index       for the 2 media involved

Example:
A ray of light strikes an air-water interface at an angle of 40 degrees from the normal. The relative refractive index for the interface is 1.33. Find the angle of refraction.

Solution:
 Write down Snell's Law Substitute in given information  (i = 40,    n* = 1.33)    Rearrange equation to get r on its own.  Turn both sides upside down to get rid of the reciprocal  Find sin 40 and calculate the value of sin r  Use the inverse sin button on your calculator to find the value for r. 