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°.

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Understanding Total Internal Reflection of Light

1. If the angle of incidence is allowed to exceed the critical angle, it is found that light rays are not refracted. This is because all of the light rays are reflected back.

2.This phenomenon is called total internal reflection.

3. Total Internal Reflection occurs when:
   a. Light rays travel from a denser medium to a less dense medium.
   b. The angle of incidence is greater than the critical angle.

Light ray which travels from a denser medium to a less dense medium will be refracted away from the normal.

Here are some Q and A session:

Q: What happens when light passes from a transparent medium into air?

A: When light passes from a transparent medium into air, it bends away from the normal. It is refracted.

Q: Why the angle of refraction becomes 90° and not more? What do we call the angle of incidence at this limit?

A: This is the limit the light ray can be refracted in air because the angle in air cannot be larger than 90°. The angle of incidence in the denser medium at this limit is called the critical angle, c.



Q: What happens when the angle of incidence is more than the critical angle?

A: When the angle of incidence is greater than the critical angle, all the light undergoes reflection.

Later we will study the Relationship between Critical angle and Refractive Index

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Analysing Reflection of Waves

1. Reflection of waves occur when a wave strikes an obstacle. The wave undergoes a change in the direction of propagation or transmission when it is reflected.

2. The incident wave is the wave before it strikes the obstacles, whereas the reflected wave is the wave after it strikes the obstacle.


3. Reflection of waves can be explained the Laws of Reflection where:

i) The angle of incidence, i is equal to the angle of reflectance, r.

ii) The incident wave, the reflected wave and the normal lie in the same plane which is perpendicular to the reflecting surface at the point of incidence.

Source: http://www.qrg.northwestern.edu/projects/vss/docs%20/media/Communications/reflection.gif

Applications of reflection of Waves in Daily Life

Safety

i) The rear view mirror and side mirror in a car are used to view cars behind and at the side while overtaking another car, making a left or right turn and parking the car. The mirrors reflect light waves from other cars and objects into the driver's eyes.

ii) The lamps of a car emit light waves with minimum dispersion. The light bulb is placed at the focal point of the parabolic reflector of the car lamp so that the reflected light waves are parallel to the principal axis of the reflector. Parallel light waves have a further coverage.

Defence

i) A periscope is an optical instrument. It can be constructed using two plane mirrors for viewing objects beyond obstacles. The light waves from an object which is incident on a plane mirror in the periscope are reflected twice before entering the eyes of the observer.

Telecommunications

i) Infrared waves from the remote control of an electrical equipment (television or radio) are reflected by objects in the surroundings and received by the television set or radio.

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Refraction of Light

Why do you think that part of a spoon that is immersed in water looks bent?

Many people think that as a stick/solid is put in liquid it becomes bent.

Do you think the same?

The reason why the spoon appears to be bent is due to the refraction of light or the bending of light. So we see spoon that appears bent in water or liquid, though in reality it is not.

What is REFRACTION OF LIGHT?

Refraction of light is a ‘bending of the light rays’ phenomena when light passes from one medium to another medium.

Refraction of light occurs when light passes through two transparent media having different densities. There are several consequences when light passes through mediums with different densities and direction.

Rays from Less Dense to Denser Medium

Q: What happens when a light ray passes through of a less dense medium into a denser medium?



A: Light rays will refract towards the normal when passing through a less dense medium into a denser medium, for example from air to glass.


Incidence Angle, Refracted Angle

The angle between the incident ray and the normal is named the angle of incidence, i.

The angle between the refracted ray and the normal is named the angle of refraction, r.



Denser to Less Dense medium

Q: What happens when a light ray passes through a denser medium into a less dense medium?

A: Light rays will refract away from the normal when passing through a denser medium into a less dense medium, for example, from glass to air.



Normal

Q: What happens when a light ray is directed to normal?
A: When light ray (incident ray) is pointed normally on a glass block, the refracted ray is unbent.




The Law of Refraction

The Law of Refraction states that:
(a) the incident ray, the refracted ray and the normal all lie in the same plane.
(b) the ratio of the angle of incidence to the angle of refraction for a given medium is fixed, that is sin i / sin r = constant.

The Law of Refraction is also known as Snell’s Law. (From dutch mathematician, Willebrord Snell)

Snell’s law states that for a light ray that passes from one transparent medium into another, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant.

The Law of Refraction is simplified as follows:
= sin i / sin r = n (a constant)

where
i = angle of incidence
r = angle of refraction
n = refractive index

A formula that is equivalent to Snell’s Law is     n1 sin i = n2 sin r
Where

n1 = refractive index of medium 1
n2 = refractive index of medium 2
i = angle of incidence
r = angle of refraction


The Refractive index

The refractive index is unitless

Here is shown the refractive index for a few materials:

Material            Refractive index
Vacuum            1.000
Air                    1.0003
Water               1.33
Ice                    1.31
Glass                1.53
Paraffin oil        1.40
Diamond          2.40

Refractive index n is defined as:
n = speed of light in medium 1 (vacuum or air) / speed of light in medium 2

Refractive index can also be represented by the following equation, Snell’s law:
n = sine of the angle of incidence, sin i /sine of the angle of refraction, sin r ( n = sin i / sin r)

Refractive index can also be determined by using:
n = Real depth, H /Apparent depth, h ( n = H/h)

Phenomena Due to Refraction of Light

The apparent Depth – A swimming Pool Looks Shallower than it Really is.

A Straight Object Placed in Water Looks Bent at the Surface (as discussed in the beginning).

Formation of Rainbow

Many more....

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Understanding the Reflection of Light: Law of Reflection of Light

1. The reflection of light can be studied by using light ray(s) and a plane of mirror which is placed on a piece of white paper.

2. When the ray of light is incident onto the surface of a plane mirror, the light ray does not pass through the mirror but is reflected back by the plane mirror.

3. The phenomena of ths experiment shows the phenomena of reflected light.

The Law of Reflection of Light States that:

1. The incident Ray, the reflected ray and the normal all lie in the same plane.

2. The angle of incidence is equal to the angle of reflection.


Image courtesy:
http://www.curriki.org/xwiki/bin/download/Coll_Athabasca/Unit3-Lesson2TheMovementofLight/reflection.jpg

More information at:

www.hsphys.com/ light_and_optics.html

Characteristics of Image that is formed on a plane mirror

1) It is upright
2) It is virtual
3) The distance form the object to the mirror is the same as the distance from the image to the mirror.
4) It is the same size as the object
5) It is laterally inverted

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