Critical Angle and Total Internal Reflection

Critical angle

When a light ray is moving from denser medium to rarer medium, it moves away from the normal. As the angle of incidence increases, angle of deviation also increases.

With the increase of angle of incidence angle of reflection in this case also increases. At a particular angle of incidence, angle of refraction becomes 90° and the light Ray grazes the boundary that is operating the two media. This particular angle of incidence is called critical angle. At the critical angle light Ray, goes exactly on the surface of the line separating the two media. Therefore at the critical angle angle of refraction is 90°. The reflected light rail is neither going into the rarer medium nor staying in the denser medium.

Total internal reflection

When a light ray is moving from denser medium to rarer medium, it moves away from the normal. With the increase of angle of incidence, angle of refraction also increases. For a particular angle of incidence called critical angle, angle of refraction is 90° and the light Ray just grazes the boundary that is separating the two media.

If the angle of incidence is more than the critical angle, the angle of refraction is more than 90°. Therefore even after the refraction the entire light Ray is reverted back into the denser medium.

The phenomena of the light restricting back into the denser medium when the angle of incidence is more than the critical angle is called total internal reflection. For the total internal reflection to happen there shall be two conditions satisfied.

The first condition is the light ray shall be moving from denser medium to a medium. The second condition is the angle of incidence shall be more than that of the critical angle.

Basing on the definition of the refractive index we can write a small equation for the critical angle as shown below.

Field vision of a fish

Let us consider a fish at a depth h from the surface of water. The fish would like to observe the surroundings in air media above the water. Hence it starts passing the light rays from the water into the air that is from denser medium to rarer medium.

The fish is able to see the surroundings above the surface of water until its angle of incidence is less than equal to critical angle. Once if the angle of incidence crosses the critical angle, the entire light rays are reflected back into the water. This is due to the phenomena of total internal reflection. Therefore the fish is able to see the surroundings only until the angle of incidence is equal to critical angle. Taking this concept into consideration and by some simple mathematical equations we can derive the equations for the Field vision of a fish as shown below.

Once if we are able to calculate the radius up to where the fish can see, we can calculate the area of the vision and that area is called Field vision of fish.