Introduction to SAT II Physics

Since we know that the ratio of / is equal to the ration of / , and since we know

the value for , we can now calculate the value for :

Given m/s, we can also calculate that the index of refraction for the liquid

substance is 2.1, while the index of refraction for the gas substance is 1.2.

Total Internal Reflection

The sine of an angle is always a value between –1 and 1 , so for certain values of , ,

and , Snell’s Law admits no solution for. For example, suppose medium 1 is glass,

medium 2 is air and = 87º. Then the angle of refraction is given by sin = 1.6, for

which there is no solution. Mathematicians have not yet invented a physical angle with
this property, so physicists just shrug their shoulders and conclude that there is no
refracted ray, which is supported by observation. This phenomenon is known as total
internal reflection.

For two given media, the critical angle, , is defined as the smallest angle of incidence

for which total internal reflection occurs. From Snell’s Law, we know that sin = sin

/ , so refraction occurs only if sin / ≤ 1. Setting the left side of that equation

to equal 1 , we can derive the critical angle:

EXAMPLE

The index of refraction for water is 1.3 and the index of refraction for air is 1.0. What is the

maximum angle of incidence at which a ray of light can pass from water into the air?

If the angle of incidence is greater than the critical angle, then the ray of light will not be
refracted into the air. The maximum angle of incidence, then, is the critical angle.