When light travels from a more dense medium to a less dense medium,
the path it follows bends away from the normal line, i.e. i <
r. This is the case when light travels from water to air (see
refraction - water to air).
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.
The cricital angle can be calculated for any given interface using an adaptation
of Snell's Law. See the example
n* = Relative refractive index (water-air interface)
ic = Critical angle
r = Angle of refraction
Note: sin 90 = 1
The critical angle for this water-air interface is 48.75 degrees.
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
When the angle of incidence is greater than the critical
angle, no refraction occurs. Instead, the incident beam is reflected, obeying
the Law of Reflection. This is called
Total internal reflection.
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.
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.