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 a 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 into an observer’s eyes so that an observer looking down at the distant ground sees light from the sky.

The image of sky where the distant ground should be produces 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.

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.

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.

2.This situation is named as 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.

Reflection of Light on a Curved Surface: Method to draw ray diagrams

1. There are two main types of curved mirrors, namely:

(a) Convex Mirror(b) Concave Mirror

2. On a Concave mirror, the rays that are parallel and close to the main axis (small opening) converge to a point F (main or principal focus) and the distance FP is known as the focal distance of the concave mirror. (P is the surface of the mirror)

More notes can be found here:http://www.glenbrook.k12.il.us/GBSSCI/PHYS/class/refln/u13l3d.html

3. On a Convex mirror, parallel rays that are close to the main axis, diverge from the surface of reflection. The rays are seen to diverge from a poinf F (main focus) behind the mirror. The distance FP is known as the focal length of the mirror.

Characteristics of Image formed by a plane mirror

Characteristics of image formed in a plane mirror.

(a) It is virtual(b) Has the same size as the object(c) Is laterally inverted (i.e. inverted sideways)(d) The distance of the object from the mirror is equal to the distance of the image form the mirror.

Refraction of Light

Why do you think a part of spoon that is immersed in water is 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 bent is due to the refraction of light or the bending of light. So we see the a bent spoon, though in reality it is not.

The phenomenon is due to

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

Less Dense to Denser Medium

Q: What happen when light rays passing through from a less dense medium into a denser medium?

A: Light rays will refract towards the normal when passing through from 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 incident ray and the normal is named the angle of refraction, r.

Denser to Less Dense

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

Normal

Q: What happen when light rays incident to normal?A: When light ray is incident 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)

wherei = angle of incidencer = angle of refractionn = refractive index

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

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

The Refractive index

The refractive index is unitless

The refractive index for a few media shown in table:

Material Refractive indexVacuum 1.000Air 1.0003Water 1.33Ice 1.31Glass 1.53Paraffin oil 1.40Diamond 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

Refractive index can also be determined by using:n = Real depth, H /Apparent depth, 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 Surfaces.

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.

image from: http://www.hsphys.com/pmirrb.jpg

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 it reflected back by the plane mirror.

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

The Law of Reflection of Light

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.