Polarisation — Wave Optics

Conceptual Foundation of Polarisation

Light is a transverse electromagnetic wave, meaning its electric field ($\vec{E}$) and magnetic field ($\vec{B}$) vectors oscillate perpendicular to each other and also perpendicular to the direction of wave propagation.

For natural light, often referred to as unpolarised light, the electric field vectors oscillate randomly in all possible directions within the plane perpendicular to the direction of propagation. Polarisation is the phenomenon of restricting these random oscillations of the electric field vector to a specific plane or a specific pattern.

When light is plane-polarised (or linearly polarised), the electric field vector oscillates along a single straight line in the plane perpendicular to the direction of propagation. If the tip of the electric field vector traces out a circle or an ellipse as the wave propagates, the light is said to be circularly polarised or elliptically polarised, respectively. For NEET, the primary focus is on plane polarisation.

Key Principles and Laws of Polarisation

Polarisation can be achieved through several methods:

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Polarisation by Selective Absorption (Dichroism):

Certain materials, known as dichroic materials, have the property of absorbing light waves whose electric field vibrations are parallel to a particular direction, while allowing light waves whose electric field vibrations are perpendicular to that direction to pass through.

The most common example is a Polaroid sheet. A Polaroid sheet consists of long-chain molecules aligned in a particular direction. It acts like a grid, allowing only the electric field components vibrating parallel to its 'pass axis' (or transmission axis) to pass through, while absorbing the components vibrating perpendicular to it.

The light emerging from a single Polaroid is plane-polarised.

* Malus's Law: When plane-polarised light of intensity $I_0$ passes through a polariser (called an analyser in this context) whose transmission axis makes an angle $\theta$ with the plane of polarisation of the incident light, the intensity of the transmitted light $I$ is given by:

This is because unpolarised light can be considered as having electric field components equally distributed in all directions. On average, half of the intensity is transmitted.

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Polarisation by Reflection:

When unpolarised light is incident on the interface between two transparent media (e.g., air to glass), the reflected light is generally partially polarised. However, at a specific angle of incidence, known as Brewster's angle ($i_p$), the reflected light is completely plane-polarised, with its electric field vibrations perpendicular to the plane of incidence (i.e., parallel to the reflecting surface). At this angle, the reflected and refracted rays are mutually perpendicular.

* Brewster's Law: Sir David Brewster discovered that when the reflected light is completely plane-polarised, the tangent of the angle of incidence is numerically equal to the refractive index of the second medium with respect to the first.

Mathematically:

This means $\sin i_p = \mu \sin r'$ and since $r' = 90^\circ - i_p$, we have $\sin i_p = \mu \cos i_p$, leading to $\tan i_p = \mu$.

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Polarisation by Refraction (Double Refraction or Birefringence):

Certain anisotropic crystals, like calcite, quartz, and tourmaline, exhibit the phenomenon of double refraction. When unpolarised light enters such a crystal, it splits into two refracted rays: an ordinary ray (O-ray) and an extraordinary ray (E-ray).

These two rays are plane-polarised in mutually perpendicular planes. The O-ray obeys Snell's law and travels with the same speed in all directions within the crystal, having a constant refractive index.

The E-ray does not obey Snell's law and travels with different speeds in different directions, thus having a variable refractive index. The O-ray and E-ray emerge from the crystal as two distinct, plane-polarised beams.

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Polarisation by Scattering:

When light passes through a medium containing particles whose size is comparable to the wavelength of light (e.g., molecules in the atmosphere), it gets scattered. The scattered light, when viewed at $90^\circ$ to the direction of incident unpolarised light, is found to be partially or completely plane-polarised.

This is why the sky appears blue (due to scattering of blue light) and why the light from the sky, when viewed through a polaroid, shows varying intensity depending on the orientation of the polaroid.

The electric field components parallel to the direction of observation are absorbed, while those perpendicular are scattered.

Real-World Applications

Polarisation is not just a theoretical concept; it has numerous practical applications:

Polaroid Sunglasses: — Reduce glare from horizontal surfaces (like water or roads) by blocking horizontally polarised light, improving visibility and reducing eye strain.
LCD Displays: — Liquid Crystal Displays (LCDs) rely heavily on polarisation. They use two polarising filters, one at the front and one at the back, with liquid crystals between them. By applying voltage, the orientation of the liquid crystals can be changed, rotating the plane of polarisation of light, thereby controlling which light passes through the second filter to create images.
3D Movies: — Some 3D movie systems use circularly polarised light. Each eye is given a different polarisation filter, allowing each eye to see a slightly different image, creating the illusion of depth.
Stress Analysis (Photoelasticity): — Transparent plastic models of mechanical parts are placed between two crossed polarisers and subjected to stress. The stress induces birefringence in the plastic, causing different colours to appear, which helps engineers visualize stress distribution and identify weak points.
Chemical Analysis (Polarimetry): — Many organic molecules, particularly sugars and amino acids, are optically active, meaning they can rotate the plane of plane-polarised light. A polarimeter measures this rotation, which can be used to determine the concentration of a solution or identify unknown substances.
Photography: — Polarising filters are used on camera lenses to reduce reflections from non-metallic surfaces (like water or glass) and to enhance the saturation of colours in the sky and foliage.

Common Misconceptions

Polarisation vs. Intensity Reduction: — While polarisers do reduce light intensity, not all intensity reduction is due to polarisation. For example, a neutral density filter reduces intensity without polarising the light. Polarisation specifically refers to the orientation of electric field vibrations.
Unpolarised Light vs. Circularly Polarised Light: — Unpolarised light has random, rapidly changing orientations of its electric field vector. Circularly polarised light has a well-defined, rotating electric field vector, where the magnitude remains constant, but its direction rotates at the frequency of the wave. They are fundamentally different.
Brewster's Angle and Total Internal Reflection: — Both involve critical angles, but they are distinct phenomena. Brewster's angle relates to complete polarisation of reflected light, while total internal reflection occurs when light travels from a denser to a rarer medium at an angle greater than the critical angle, resulting in no refraction.

NEET-Specific Angle

For NEET, a strong conceptual understanding of each method of polarisation is crucial. Students should be able to:

Identify the type of polarisation produced by each method (e.g., reflection produces plane-polarised light perpendicular to the plane of incidence at Brewster's angle).
Apply Malus's Law correctly to calculate intensity after passing through one or two polarisers.
Calculate Brewster's angle given the refractive index, and vice-versa.
Understand the behaviour of O-ray and E-ray in birefringent crystals.
Recognize real-world applications and their underlying polarisation principles.
Distinguish between unpolarised, plane-polarised, circularly polarised, and elliptically polarised light.
Solve problems involving multiple polarisers and varying angles.