# Refractive index:

Refractive index is defined as the measure of the bending of light when passes from one medium to another. Refractive index is equal to the velocity of light c divided by its velocity v in substance .

n= c/v

The Refractive index of any substance depends upon:

• The nature of substance
• temperature
• the wave length of light used.

#### Reflection in Refractive index :

Whenever a beam of monochromatic light passes from one medium into the other. It suffers a change in the direction of propagation.

Now this change of direction is known as Reflection. It depends upon the nature of the two media and direction in which the light travels.

When a ray of light passes from a rare to a denser medium , it bends towards the normal at the point of incidence, as shown fig.

According to snell’s law, the ratio of the sine of angle of incidence and that of refraction is constant and characteristic for that medium.

N =   Sin i|Sin r

#### The wave theory of light:

According to the wave theory of light, the ratio of the sines of the angles of incidence and refraction is identical with the ratio of the velocity of light in the two media. Thus ,

n= sin i /sin r = velocity in air / velocity in liquid

According to the law of refraction,

Sin i/Sin r = n2/n1

#### Critical angle :

Where n1 is the refractive index of the rare and n2 the refractive index of the denser medium. The angle of refraction is also rising as the angle of incidence increases. When i= 90 degree , r reaches its maximum value and it is known as the critical angle.

Since sin 90 = 1

We can write above equation like,

Sin r = n1/n2

If the angle of incidence is greater than 90, the ray is totally reflected. Most of the refractometers work on the principle of critical angle for measuring refractive index of a medium.

### Measurement of refractive index:

The refractive indices of liquids can be measured directly with calibrated instrument called refractometer.

Two refractometer commonly used:

1. Abbe Refractometer
2. Pulfrich Refractometer

### Abbe Refractometer :

A general sketch of the Abbe refractometer is shown in the fig.

The optical system of the abbe refractometer consists of three parts

1. A mirror M,
2. two prism A and B housed in a box hinged at H
3. A fixed telescope T and an eye-piece O.

The two prisms faces can be held in contact with the knob c. To the box carrying the graduated scale S, a direct reading on the scale gives the refractive index.

### Procedure Refractive index:

The prism box is opened , a drop of the test liquid is placed between the two prisms and then the box is closed.

The cross wire of the telescope are focused by rotating the eye-piece and the mirror is adjust for the maximum illumination. The prism box slowly moved backwards and forward by means of the knob C. Until the field of view becomes partly dark and partly bright .

When the white light is used the coloured fringes observed are removed by rotating the compensator and a sharp line will divide the bright and dark portations.

The Prism box is then rotated until the end of the bright portion coincides with point of intersection of the cross – wires of the telescope. The refractive index is reported directly on the eye-piece O scale.

We see that refractive index is affect by the temperature and wavelength of light. In order to maintain consistency of temperature and wavelength , prism A and B are enclose in water jacket J and sodium or mercury light is preferably use.

### Pulfrich Refractometer:

Pulfrich refractometer is in theory very reliable and simple for the calculation of liquid refractive indices. The basic design of the instrument is showns.

The essential part of the instrument is a right angles glass prism with a small glass cell cemente to its top.

The liquid to be examined is placed in the glass cell and beam of monochromatic light is made to enter at ‘grazing incidence ,along the surface between the liquid and the prism. It follows the path ABCD and is observe by a telescope at D.

If r be the angle of refraction when the angle of incidence is 90 degree.

Then ,

Sin r = n1/n2

Where n1 is the refractive index of the liquid and n2 that of the glass prism.

Sin i/Sin (90 – r) = n2

If the refractive index n2 of the prism is known and the angle i is the measure the refractive index of the liquid , can be calculated .

In practice , tables of n2 – sin i , putting the refractive indices from the values of the measured angle i.

#### Refractive index and Composition :

The refractive index of a liquid varies with the wavelength and also with the temperature. To eliminate the effect of temperature , Lorentz and Lorenz (1880) derived a relationship between refractive index and density of a liquid.

R = n2 – 1 /n2 +2 × 1/D

Where R is a specific refraction and refractivity ,Which is independent of temperature,n is the refractive index and d is the density of the liquid.

For comparison molar refraction or molar refractivity Rm is employe which is equal to the product of the specific refraction and molar mass.

I.E.

Rm = n2 – 1 /n2 +2 × M/D

The molar refraction like specific refraction is temperature independent , but depends upon the wavelength of light used for measuring the refractive index .

It is for this reason that the molar refractions are generally reporte for a definite wavelength.

E.g
α- or β- hydrogen or sodium lines D.

Since refractive index is dimensionless, the units of molar refraction are the units of M/d i.e..,Volume expressed in cubic meter per mole . The molar refraction is an additive and constitutive property.

This molar refraction of a molecule can thus be consider to be a sum of refractions of the atoms and bond existing in the molecule.