The waves that travel down a string when you shake it are called transverse waves since the displacement of each particle in the string is perpendicular to the direction of propagation. E.g. light wave.

There are another set of waves known as longitudinal waves whose displacement from equilibrium position is along the direction of propagation. E.g. sound wave.

Why polarization is observed in transverse waves only?

Definition of polarization

Polarization is a method of confining a particular set of vibrations at any instant of time. It is observed in transverse waves only.

Polarization vector defines the plane of vibration and it is perpendicular to the direction of propagation.

Now, the question arises as to why polarization is an exclusive property of transverse waves.

Transverse waves vibrate in a direction perpendicular to the direction of propagation. There are two directions perpendicular to a line of propagation. Hence, it is possible to confine a particular set of vibrations at any instant of time by cutting off the other set.

This method is exclusive to transverse waves as there are 2 possibilities for doing that. If direction of propagation is in X-direction then vibrations can be in either Y-direction or Z-direction. We can then restrict the vibrations either along Y-direction or Z-direction.

However, the same method is not applicable to longitudinal waves since their displacement is along the direction of propagation. If we have to confine that direction along which it travels then it would stop travelling altogether.

We are aware that in electromagnetic waves, magnetic field, electric field and direction of propagation are mutually perpendicular. At any instant of time, Electric field vector and magnetic field vector vibrate in every possible direction.

This is for an un-polarized light.

Polarization in Electromagnetic Waves

It is possible to polarize light in two different ways, they are:

Plane Polarized light

In a plane polarized light, electric field vector vibrates along a specific direction as time passes by. In other words, the trajectory followed by the electric field vector is a straight line.

Circularly polarized light

In a circularly polarized light, electric field vector rotates with time. In other words, the trajectory followed by electric field vector is a circle.

Equation for plane polarized light

We see that ration of (Y/X) remains same throughout, tip of the vector moves along a straight line.

E_y= E_x. .....................equation of straight line.

Circularly Polarized Light

EQUATION:

Above is the equation of circle.

If tip of the electric field vector moves clockwise, it is right circularly polarized.

If tip of the electric field vector moves anti-clockwise, it is left circularly polarized light.

Note, that in circularly polarized light, the amplitudes of both E_X and E_Y are same. Had they been different, then it would have been elliptically polarized light.

In other words, circularly polarized light is a special case of elliptically polarized light.

HOW TO DETERMINE STATE OF POLARIZATION JUST BY LOOKING AT THE EQUATION?

• If the phase difference between x and y components of electric field vector is odd multiple of p/2, then state of polarization would be either circular/elliptical.
• If the phase difference between x and y components of electric field vector is even multiple of p/2, then state of polarization would be linear.
• If the phase difference between x and y components of electric field vector are arbitrary, then state of polarization would be elliptical.