optics8

Chapter III

OPTICS

Lecture 3.8

Books:(i) Optics, 3

edition: Ajoy Ghatak, McGraw-Hill

Companies

Here we shall discuss about:

•_Polarization

•Phenomena of double refraction • _{Nicol prism}

•_{Production and analysis of plane}

Polarization:

If we move one end of a string up and down, then a transverse wave is generated [see Fig. ].

The transverse wave is the one in which particles of the medium move in a direction perpendicular to the direction of propagation of waves whereas in case of longitudinal

(a) A x-polarized wave on a string with the displacement confined to the xz plane.

The each point of the string executes a sinusoidal oscillation in a straight line (along the x axis), and the wave is, therefore, known as a linearly polarized wave. It is also known as a plane

polarized wave because the string is always confined to the xz plane.

The displacement for such a wave can be written in the form,

where a represents the amplitude of the wave and ɸ is

(a) The displacement

corresponding to a circularly polarized wave.

All points

on the string are at

the same distance from the z axis.

(b) Each point on

Now we consider a long narrow slit placed in the path of the string as shown in Fig.

If the length of the slit is along the

direction of the displacement, then the entire amplitude will be transmitted as shown in Fig(a).

On the other hand, if the

slit is at right angles to the direction of the displacement, then

almost nothing will be transmitted

to the other side of the slit fig (a) [see Fig. (b)]

This is so because the slit allows only the

component of the displacement, which is along the length of the slit, to pass through.

However, if a longitudinal wave were

propagating through the string, then the amplitude of the transmitted

wave would have been the same for all orientations of the slit.

Thus, the change in amplitude of the transmitted wave

Now we consider transverse waves generated at

one end of a string. If the plane of vibration is changed in a random manner in very short intervals of

time, then such a

wave is known as an unpolarized wave.

If an unpolarized

wave falls on a slit S1 (see Fig. ), then the displacement

associated with the transmitted wave is along the length of

Thus, the transmitted wave is linearly polarized, and slit S₁ is

said to act as a polarizer.

If this polarized beam falls on another

slit S₂ (see Fig. On last slide) , then by rotating slit S₂ we obtain a variation of the transmitted amplitude as discussed earlier.

The light waves (electromagnetic waves) are transverse in nature.

These waves are characterized by electric and magnetic field vectors which are perpendicular to each other and also

Let us consider an ordinary light beam falling on a Polaroid P1 as shown in Fig (a).

Note that a Polaroid is a plastic like material used for producing polarized light.

In general, an ordinary light beam (such as the one coming from a sodium lamp or from the sun) is unpolarized i.e. the electric

vector (in a plane transverse to the direction of propagation) keeps changing its direction in a random manner [see Fig(2.b) ].

When such a beam is incident on a Polaroid, the emergent light is linearly polarized with its electric vector oscillating in a particular direction as shown in Fig. (a) [see also

Fig. (2.b)].

The direction of the electric vector of the emergent beam will depend on the orientation of the Polaroid.

The component of E along a particular direction gets absorbed by the Polaroid, and the component at right angles to it passes through.

The direction of the electric vector of the emergent wave is

usually called the pass axis of the Polaroid. if the position of the eye is as shown in the figure, then one

will observe no variation of intensity if the Polaroid is rotated about the z axis.

Now we place another Polaroid P2

[see Fig. (b)]. Now by rotating the Polaroid P2 (about the z axis) we will observe variation of intensity.

when the two Polaroids are perpendicular to each other, no light will pass through the second Polaroid [see fig (c)].

A similar phenomenon will also be observed if instead of rotating the Polaroid P₂ we rotate P₁.

This phenomenon proves the transverse character of

light; i.e., the displacement associated with a light wave is at right angles to the direction of propagation of the wave.

The Polaroid P₁ acts as a polarizer, and the transmitted beam is

From above discussion we have following conclusions:

_{The unpolarised light is the one in which waves has infinite}

number of orientations. So there is symmetry.

_{In polarized light, there is lack of symmetry about the direction of}

Propagation of light.

_{When the vibrations are confined along a single directions at right}

Angle to direction of propagation then light is said to be plane Polarized.

The plane in which the vibrations of the polarised light are confined is known as plane of vibrations.