Polarization
Consider holding a long string that is held horizontally, the other end of which is assumed to be fixed. If we move the end of the string up and down in a periodic manner, we will generate a wave propagating in the +x direction (Fig.1). Such a wave could be described by the following equation
`y (x,t ) = a sin (kx - ωt)......(1)`
where `a` and `ω (= 2πnu )` represent the amplitude and the angular frequency of the wave, respectively; further,
`lamda=(2pi)/k........(2)`
represents the wavelength associated with the wave.
Since the displacement (which is along the y direction) is at right angles to the direction of propagation of the wave, we have what is known as a transverse wave. Also, since the displacement is in the y direction, it is often referred to as a y-polarized wave. Since each point on the string moves on a straight line, the wave is also referred to as a linearly polarized wave. Further, the string always remains confined to the x-y plane and therefore it is also referred to as a plane polarized wave.
In a similar manner we can consider the vibration of the string in the x-z plane generating a z-polarized wave whose displacement will be given by
`z (x,t ) = a sin (kx - ωt )......(3)`
It should be mentioned that the linearly polarized waves [described by Eqs. (2) and (3)] are all transverse waves; i.e., the displacement of each point of the string is always at right angles to the direction of propagation of the wave. Finally, if the plane of vibration of the string is changed randomly in very short intervals of time, then we have what is known as an unpolarized wave. Thus, for an unpolarized wave the displacement will be randomly changing with time though it will always be perpendicular to the direction of propagation.
Light waves are transverse in nature; i.e., the electric field associated with a propagating light wave is always at right angles to the direction of propagation of the wave. This can be easily demonstrated using a simple polaroid. You must have seen thin plastic like sheets, which are called polaroids. A polaroid consists of long chain molecules aligned in a particular direction. The electric vectors (associated with the propagating light wave) along the direction of the aligned molecules get absorbed. Thus, if an unpolarized light wave is incident on such a polaroid then the light wave will get linearly polarized with the electric vector oscillating along a direction perpendicular to the aligned molecules; this direction is known as the pass-axis of the polaroid.
Thus, if the light from an ordinary source (like a sodium lamp) passes through a polaroid sheet `P_1`, it is observed that its intensity is reduced by half. Rotating `P_1` has no effect on the transmitted beam and transmitted intensity remains constant. Now, let an identical piece of polaroid `P_2` be placed before `P_1`. As expected, the light from the lamp is reduced in intensity on passing through `P_2` alone. But now rotating `P_1` has a dramatic effect on the light coming from `P_2`. In one position, the intensity transmitted by `P_2` followed by `P_1` is nearly zero. When turned by `90^@` from this position, `P_1` transmits nearly the full intensity emerging from `P_2` (Fig.2).
The above experiment can be easily understood by assuming that light passing through the polaroid `P_2` gets polarized along the pass-axis of `P_2`. If the pass-axis of `P_2` makes an angle θ with the pass-axis of `P_1`, then when the polarized beam passes through the polaroid `P_2`, the component E cos θ (along the pass-axis of `P_2`) will pass through `P_2`. Thus, as we rotate the polaroid `P_1` (or `P_2`), the intensity will vary as:
`I=I_0cos^2theta.......(4)`
`y (x,t ) = a sin (kx - ωt)......(1)`
where `a` and `ω (= 2πnu )` represent the amplitude and the angular frequency of the wave, respectively; further,
`lamda=(2pi)/k........(2)`
represents the wavelength associated with the wave.
Since the displacement (which is along the y direction) is at right angles to the direction of propagation of the wave, we have what is known as a transverse wave. Also, since the displacement is in the y direction, it is often referred to as a y-polarized wave. Since each point on the string moves on a straight line, the wave is also referred to as a linearly polarized wave. Further, the string always remains confined to the x-y plane and therefore it is also referred to as a plane polarized wave.
In a similar manner we can consider the vibration of the string in the x-z plane generating a z-polarized wave whose displacement will be given by
`z (x,t ) = a sin (kx - ωt )......(3)`
It should be mentioned that the linearly polarized waves [described by Eqs. (2) and (3)] are all transverse waves; i.e., the displacement of each point of the string is always at right angles to the direction of propagation of the wave. Finally, if the plane of vibration of the string is changed randomly in very short intervals of time, then we have what is known as an unpolarized wave. Thus, for an unpolarized wave the displacement will be randomly changing with time though it will always be perpendicular to the direction of propagation.
Light waves are transverse in nature; i.e., the electric field associated with a propagating light wave is always at right angles to the direction of propagation of the wave. This can be easily demonstrated using a simple polaroid. You must have seen thin plastic like sheets, which are called polaroids. A polaroid consists of long chain molecules aligned in a particular direction. The electric vectors (associated with the propagating light wave) along the direction of the aligned molecules get absorbed. Thus, if an unpolarized light wave is incident on such a polaroid then the light wave will get linearly polarized with the electric vector oscillating along a direction perpendicular to the aligned molecules; this direction is known as the pass-axis of the polaroid.
Thus, if the light from an ordinary source (like a sodium lamp) passes through a polaroid sheet `P_1`, it is observed that its intensity is reduced by half. Rotating `P_1` has no effect on the transmitted beam and transmitted intensity remains constant. Now, let an identical piece of polaroid `P_2` be placed before `P_1`. As expected, the light from the lamp is reduced in intensity on passing through `P_2` alone. But now rotating `P_1` has a dramatic effect on the light coming from `P_2`. In one position, the intensity transmitted by `P_2` followed by `P_1` is nearly zero. When turned by `90^@` from this position, `P_1` transmits nearly the full intensity emerging from `P_2` (Fig.2).
The above experiment can be easily understood by assuming that light passing through the polaroid `P_2` gets polarized along the pass-axis of `P_2`. If the pass-axis of `P_2` makes an angle θ with the pass-axis of `P_1`, then when the polarized beam passes through the polaroid `P_2`, the component E cos θ (along the pass-axis of `P_2`) will pass through `P_2`. Thus, as we rotate the polaroid `P_1` (or `P_2`), the intensity will vary as:
`I=I_0cos^2theta.......(4)`