Relationship between Critical Angle and Refractive Index

Consider the equation below;

but:

Then,

According to the principle of reversibility of light (the path can be reversed)

ퟏ

풂휼

=

Therefor:e

푾

풔풊풏풄

 This is true for all material media where, water, w represents

material media

Conditions for total internal reflection to occur

• Light must be travelling from an optically denser medium (higher refractive

index) to an optically less dense medium (lower refractive index) (e.g glass

to air)

• The angle of incidence should be equal or greater than the critical angle for

the two media

Some effects of total Internal Reflection of Light

(a) Mirage

• This is an impression of the presence of imaginary water some distance away

• OR - Mirage Is an optical phenomenon in the atmosphere that makes an

object appears to be displaced from its true position.

• This happens when air nearer the surface of the ground is less dense than

the air above. Cool air is dense than warm air

• Light from the sky is gradually refracted away from the normal as it passes

from denser layer of air to less dense layers

• When light meets a layer at angles of incidences greater than the critical

angle. It suffers total internal reflection

• Thus, the reflection of the sky forms an image which appears as a pool of

water on the road  Mirages are often seen during hot sunny days.

(b) Atmospheric Refraction

• Since we know the change in medium causes refraction likewise our earth is

covered with the atmosphere having different layers, and these layers

possess different temperatures at different heights, some atmospheric

layers are warm and some are cold.

• Now the warmer layer of the atmosphere behaves like an optically rarer

medium whereas the cooler layer behaves like an optically denser medium.

• So now we again have different media thus when light passes through

different layers of the atmosphere it gets refracted.

Examples of Atmospheric Refraction

• Twinkling of stars. This happens when the atmosphere refracts more light to

us the star seems bright. However, when the atmosphere refracts less light

than the star seems dim, and this process happens so fast that it seems to

us twinkling.

• The apparent position of the stars: As we discussed in the twinkling of a

star that our atmosphere has different layers which cause light to refract, so

our atmosphere bends the starlight towards normal, which causes the

apparent position of the star to appear to be slightly different from its actual

position.

• Bending of Sun’s Rays:

Air is slightly more optically dense than a vacuum, this means that when

sunlight passes from the vacuum of space into our atmosphere it bends

slightly towards the normal. When the sun is below the horizon and thus not

visible on a direct line, some of the light entering the atmosphere will refract

and remain visible to us. Observers can see the sun before it actually comes

up over the horizon, or for a short time after it sets.

• The Rainbow: The formation of a rainbow involves Reflection, Refraction,

and Dispersion. Firstly, the sunlight enters into the water droplet during which

it undergoes refraction as well as dispersion. So, the light bends inside the

droplet (due to change in medium) and performs total internal reflection and

then comes out where the light again refracts which results in the formation of

a rainbow.

(c) A swimming pool always seems or looks much shallower than it really is

because of the light that comes from the bottom of the pool bends at the surfaces

due to the refraction of light.

Applications of total internal Reflection

1.Prism periscope

• A periscope is a device which enables us to see over the top of an obstacle

• A prism periscope consists of two 45° - 90° - 45⁰prisms (See the fig below)

• Prisms are used in the construction of a periscope. The image seen through

a periscope is upright and the same size as the object.

• The first prism rotates the image by 90° and the second prism rotates it back

to normal.

2.Optical fibres

• An optical fibre is a thin rod of high-quality glass designed to guide light along

its length by total internal reflection.

• Light inside these fibres hits the sides at an angle greater than the critical angle

and is transmitted by being repeatedly totally internally reflected.

Some uses of optical fibres

• Are used in telecommunications and networking to send message signals.

• They are also used as light guides in medical and other applications

• Optical fibres are also used in imaging optics. A bundle of fibres along with

lenses are used to make a long imaging device called an endoscope. An

endoscope is an instrument made of a fibre optic cable. It is used by doctors to

see the inside of the human body such as the stomach and the duodenum. NB:

✓ Medical endoscopes are used in minimally invasive surgical procedures.

✓ Industrial endoscopes are used for inspecting machine parts

✓ Advantages of using optic fiber rather than copper cables

(i)

Have high speed. Fiber optic cables transmit data much faster than

copper wires do because fiber optics uses the speed of light rather

than the speed of electrons. Fiber optic Internet connections can

range from 5 Mbps to 100 Gbps. This ensures no wasted time or

productivity due to a slow Internet connection. Fiber optic cables also

enable “symmetric speed,” which means that uploading and

downloading speeds are equal.

(ii)

High security. Because fiber optic cables cannot be tapped easily,

this makes them the ideal option for high Internet security. The only

way to penetrate a fiberoptic Internet connection is to cut the wires,

which will make the signal disappear

This is important for sensitive applications such as financial

transactions and government communications.

(iii)

(iv)

Copper cables are typically thicker and heavier than fiber optic cables,

making them less convenient for installations that require lightweight

and slim cabling.

Distance: Fibre optic cabling is capable of transmitting data over

significantly longer distances without signal degradation. They are

often used for long-distance communication, including undersea

cables. Copper cabling, on the other hand, has distance limitations,

with the quality of data transmission diminishing over greater

distances.

(v)

High Bandwidth: Fiber optic cables have a much higher bandwidth

than copper wires, which means they can carry more data at faster

speeds. This enables the transmission of high-bandwidth content

such as high-definition video and large data files. This makes optical

fiber an essential component of modern communication networks.

Binoculars and telescopes

• Binoculars are just a pair of telescopes one for each eye.

• A 45°/45° prism can cause light rays to bend through 180° when the light is

incident at right angles onto the hypotenuse of the prism as shown in Figure.

• This property of prisms makes them useful in the construction of binoculars.

• Two prisms are arranged to bend the light rays from an object through 360°.

• A pair of binoculars is much more compact than a telescope.

• Binoculars are used to see distant objects