Polarisation of Light

Polarisation is the phenomenon of restricting the vibration of a light wave to a particular plane perpendicular to the direction of propagation of the wave, or confining the electric vector vibrations to one direction perpendicular to the direction of propagation.

An unpolarised wave is one in which the plane of vibration changes randomly in very short time intervals.

A transverse wave is one in which the displacement of particles is perpendicular to the direction of propagation of the wave.

A wave in which the electric field vectors are confined in one plane and are parallel to a unique direction is called a linearly polarised wave or plane polarised wave.

A Polaroid is a thin film of ultramicroscopic crystals used to produce plane-polarised light.

The plane of vibration is the plane in which the electric field vector \[\vec{E}\] vibrates or oscillates.

The plane of polarisation is the plane in which vibrations are present — it is perpendicular to the plane of vibration and contains the direction of propagation.

Statement

When a beam of plane polarised light is incident on an analyser, the intensity of the transmitted light is directly proportional to the square of the cosine of the angle θ between the pass-axis of the analyser and the plane of polarisation of the incident light.

Three polaroids are used:

• P₁ polarises the unpolarised light.
• P₂ is placed between P₁ and P₃ and can be rotated.
• P3 is crossed with P₁ (their pass axes are at 90°), so without P₂, no light passes through.

When P₂ is rotated by an angle θ:

• The light intensity after P₂ becomes: I = I₀ cos^⁡2 θ
• The light then passes through P₃, giving the final intensity:
  I = \[I_0\cos^2\theta\sin^2\theta=\frac{I_0}{4}\sin^22\theta\]

The transmitted intensity is maximum when:

θ = 45^∘ (\[\frac {π}{4}\])

Conclusion:
When the middle polaroid (P₂) is rotated to 45°, the maximum amount of light passes through all three polaroids, even though the first and third polaroids are crossed.