Relationship between Critical angle and Refractive Index and Application of Total Internal Reflection

Let’s say that the less dense medium is air (n=1).

Then the refractive index of the second medium is:

n = sin i /sin r

   = sin 90° / sin c

n =  1 / sin c

So,

REFRACTIVE INDEX :

n =  1 / sin c     or 1 divided by sin c

c = critical angle for the medium

Refractive Index, n, for some materials and their critical angles

Material Refractive       Index (n)        Critical angle (c)
Water                              1.33                  48.8°
Glass                               1.50                   41.8°
Diamond                         2.42                   24.4°

Example:

If the critical angle for a material is 42°. What is it’s refractive index?

n = 1 / sin c
   = 1 / sin 42°
   = 1.49

What do you think the material is?

Yes, the refractive index is 1.49 nearing to 1.50 therefore from the table above, the material is most probably glass.

Phenomena of Total Internal reflection

Diamonds

• Brilliant diamonds have a high index of refraction.
• Light entering a cleaved, or cut, diamond from the top may also eventually exit the top.
• This gives a false notion of internal sparkle.
• Colored flashes of light occur in a fiery diamond when light is separated into colors.

Rainbow formation

When sunlight shines on raindrops, refraction and total internal reflection occur in the raindrop.
When an observer receives the refracted light from the rainbows at specific angle, a vision of rainbow is formed.

Mirage

A mirage occurs when an object appears displaced from its true position.

Atmospheric mirages are created when light is bent, or refracted, as it travels through layers of air with differing densities.

Changes in air density are usually caused by changes in air temperature.

If the air near the ground is much warmer than the air above, light from the sky will bend up towards an observer’s eyes so that an observer looking down at the distant ground sees light from the sky.

The image of sky is shown as the mirage of a watery pavement, or water resting on hot desert sand.

When the light from an object is bent, making the object appear higher than it actually is, a superior mirage occurs.

When an object appears lower than it actually is, the mirage is called an inferior mirage.

Application of Total Internal Reflection

Fibre Optics

Fiber-Optics make use of total internal reflection to guide light along transparent fibres.

A strand of fiber-optic cable reflects the light that passes through it back into the fiber, so light cannot escape the strand.

Fiber-optic cables carry more information than conventional cable.

USES:

Communication – used in internet and telephone cables, t v cables.

Other uses –
Transmission of light to places which is difficult to illuminate e.g. dentist’s drill.
Endoscope – used to see internal organs of the body.

Binoculars

Binoculars are used to see distant objects.

There are two prisms arranged specially in each half of the binoculars.

Light rays from distant objects undergo total internal reflection in the prisms before entering the eyes of the observer.

The image seen by the observer is erect.

Example of Questions:

A glass block has a refractive index of n = 1.52. Calculate the critical angle c for this glass.

The critical angle for water is 49°.