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Critical Angle

The angles of incidence and refraction can have values between 0 and 90 degrees. When the angle of refraction is 90 degrees, the refracted beam travels along the interface. Given that  i < r ,  when  r = 90,   i = < 90. The angle of incidence which results in  r = 90 is refered to as the critical angle and is given the symbol ic.
 

Calculating Critical Angle

where:  n* =  Relative refractive index (water-air interface)      =   0.752  ic  =  Critical angle  r   =  Angle of refraction  Note: sin 90 = 1

What would happen if the incident ray hit the interface at a angle greater than 48.75 degrees? Maybe you could devise an experiment to find out! Alternatively, you could read on about Total Internal Reflection (TIR).

Total Internal Reflection

Total Internal Reflection in Rainbows.

In the formation of a rainbow, Total Internal Reflection occurs at the rear of   the raindrop - the water-to-air interface. Therefore, in order for a rainbow to be visible, the angle of incidence at that interface must be greater than the critical angle. See diagram.

 

Example of Total Internal Reflection (animation)

Below is an example of total internal reflection at a water-to-air interface with a relative refrative index of  0.752. All of the angles have been calculated using Snell's Law. The angles are to scale, you can see this for yourself by placing a transparent protractor over the screen. Note that the critical angle is 48.75 degrees as calculated above.