Wave Optics | Class 12 Physics Notes

10.7 POLARISATION

Polarisation is a phenomenon observed in transverse waves where the oscillations occur in a particular direction. Consider a string fixed at one end; if the free end is moved up and down periodically, a sinusoidal wave propagates along the string with displacement perpendicular to the direction of propagation. This is a linearly polarized wave with displacement in the y-direction.

The wave can be described by y(x, t) = a sin(kx - ωt), where a is amplitude, k is wave number, ω is angular frequency, and λ = 2π / k is wavelength.

Similarly, if the string vibrates in the x-z plane, the displacement is z(x, t) = a sin(kx - ωt), representing z-polarized waves. Both are transverse waves with displacement perpendicular to propagation.

If the plane of vibration changes randomly and rapidly, the wave is unpolarised, with displacement directions varying randomly but always perpendicular to propagation.

Light waves are transverse electromagnetic waves with electric field vectors oscillating perpendicular to the direction of propagation. Polaroids are sheets with aligned molecules that absorb electric vectors parallel to their alignment, transmitting only components perpendicular to it, thus polarising light.

When unpolarised light passes through a polaroid, its intensity reduces by half and becomes linearly polarised. Passing through a second polaroid with its pass-axis at angle θ to the first, the transmitted intensity varies as I = I0 cos² θ (Malus' law).

This explains the control of light intensity using polaroids, used in sunglasses, cameras, and 3D movies.

Example 10.2 discusses intensity variation when a polaroid sheet is rotated between two crossed polaroids, showing transmitted intensity varies as (I0 / 4) sin² 2θ, with maximum at θ = π/4.

📊 Diagram: Figure 10.17 (a) The curves represent the displacement of a string at t = 0 and at t = Δt, respectively when a sinusoidal wave is propagating in the +x-direction. (b) The curve represents the time variation of the displacement at x = 0 when a sinusoidal wave is propagating in the +x-direction; Figure 10.18 (a) Passage of light through two polaroids P2 and P1. The transmitted fraction falls from 1 to 0 as the angle between them varies from 0° to 90°. Notice that the light seen through a single polaroid P1 does not vary with angle. (b) Behaviour of the electric vector when light passes through two polaroids. The transmitted polarisation is the component parallel to the polaroid axis. The double arrows show the oscillations of the electric vector.

🔗 Connection: Leads to the Summary section consolidating key concepts of wave optics.