5.3 Understanding Total Internal Reflection of Light

    When light is incident upon a medium of lesser index of refraction, the ray is bent away from the normal, so the exit angle is greater than the incident angle. Such reflection is commonly called "internal reflection". The exit angle will then approach 90° for some critical incident angle θ_c , and for incident angles greater than the critical angle there will be total internal reflection. 

Critical Angle

Total Internal Reflection

Calculating the Critical Angle

Now we shall learn how to derive the value of the critical angle for two given media. The process is fairly simple and involves just the use of Snell’s Law that we have already studied.

To recap, Snell’s Law states:
n_{1 sin θ1} = n₂ sin θ₂

where n₁ is the refractive index of material 1, n₂ is the refractive index of material 2, θ1 is the angle of incidence and θ2 is the angle of refraction.

For total internal reflection we know that the angle of incidence is the critical angle.
So,
θ1 = θc.

However, we also know that the angle of refraction at the critical angle is 90◦. So we have:

θ2 = 90◦

We can then write Snell’s Law as: 

 n_{1 sin θ1} = n₂ sin 90◦ 

Critical angle and total internal reflection

When light travels from a medium of high refractive index to one of lower refractive index (e.g. glass into air), it bends away from the normal. If the angle within the medium θ_m is increased, a point is reached where the angle in θ_a becomes 90º.
The angle in the medium which causes this is called the critical angle, θ_c.
If the angle in the medium is greater than the critical angle, then no light is refracted and Total Internal Reflection takes place within the medium.

Relationship between critical angle and refractive index

At the critical angle, θ_m = θ_c and θ _a = 90º

         n =  

 

Effect of a Prism on Light Rays

The rays of light are deflected by 90º

The rays of light are inverted.An inverted image is seen.

The two rays of light are deflected by 180º. 

The two rays are inverted and an inverted image is seen.

  

 Phenomenon

total internal reflection occurs

total internal reflection occurs

Fish's Eye View

Road Mirage

Application

Optical Fibres

Prism Binoculars

Prism Periscope