Polarisation of Light

The plane containing the direction of propagation and perpendicular to the plane of vibration

Step 1: The plane of vibration is defined as the plane containing the direction of vibration of the electric vector AND the direction of propagation of light. Step 2: The plane of polarisation is perpendicular to the plane of vibration and contains the direction of propagation. Crucially, there are NO vibrations in the plane of polarisation. Step 3: Option (a) describes the plane of vibration, not the plane of polarisation. Option (c) is incorrect because E and B vibrate in mutually perpendicular planes. Option (d) is not a standard definition.

32 W/m²

Step 1: When unpolarised light passes through an ideal polaroid, the polaroid transmits only those components of the electric vector that are parallel to its polarising direction. Step 2: The average value of cos²θ over all directions is 1/2. Therefore, the transmitted intensity = (1/2) × I₀. Step 3: I = (1/2) × 64 = 32 W/m². Step 4: This means even an ideal polaroid can transmit at most 50% of incident unpolarised light. Options (c) and (d) suggest further reduction which happens only when a second polaroid is involved.

1.647

Step 1: The polarising angle for the water-glass interface is ip = 51°. By Brewster's law, the refractive index of glass with respect to water is: wnG = tan 51° = 1.235. Step 2: The refractive index of glass with respect to air is found using: anG = anW × wnG. Step 3: anW = 4/3 = 1.333 (given). Step 4: anG = 1.333 × 1.235 ≈ 1.647. Option (a) 1.235 is the refractive index of glass with respect to water, not air. Option (c) 1.333 is the refractive index of water. Option (d) is the reciprocal of wnG.

Transverse waves

Step 1: Polarisation is a phenomenon in which the vibrations of a wave are restricted to a single direction perpendicular to the direction of propagation. Step 2: Only transverse waves can be polarised, because in transverse waves, vibrations occur perpendicular to the direction of propagation (so they can be restricted to one direction). Step 3: Longitudinal waves have vibrations parallel to the direction of propagation. There is no 'perpendicular plane' to restrict, so they CANNOT be polarised. Step 4: Since light can be polarised, it must be transverse. Sound waves (longitudinal) cannot be