Revision: Class 12 >> Diffraction and Polarisation of Light NEET (UG) Diffraction and Polarisation of Light

The type of diffraction that occurs when the source or screen is at a finite distance from the diffracting object and fringes are not sharp and well-defined is called Fresnel diffraction.

The type of diffraction that occurs when the source and the observation screen are far away (effectively at infinite distance) from the diffracting object and fringes are not sharp and well-defined is called Fraunhofer diffraction.

The bending of light near the edge of an obstacle or slit and spreading into the region of geometrical shadow is called diffraction of light.

A thin film of ultramicroscopic crystals used to produce plane polarised light is called a polaroid.

When the plane of vibration of a wave is changed randomly in very short intervals of time, such waves are called unpolarised waves.

The plane in which vibrations are present is called the plane of polarisation.

The phenomenon of restriction of the vibration of light waves in a particular plane perpendicular to the direction of wave motion is called polarisation of light.

or

The phenomenon of confining the vibrations of the electric vector to a particular direction perpendicular to the direction of propagation of light is called Polarization.

When the displacement of the particle is perpendicular to the direction of propagation of the wave, then it is said to be transverse wave.

The wave in which the vibration of electric field vectors are confined in one plane and parallel to one unique direction is called linearly polarised wave; it is also referred to as plane polarised wave.

The plane in which E vibrates/oscillates is known as the plane of vibration.

Alignment of dipole moments (permanent or induced) in the direction of an applied electric field is called polarisation.

Defined as dipole moment per unit volume:

\[P=\frac{\text{dipole moment}}{\mathrm{volume}}=np\]

Statement: When plane polarised light is incident on an analyser, the resultant intensity of light transmitted from the analyser varies directly as the square of the cosine of the angle between the plane of transmission axis of the analyser and polariser.

Formula:

Where:

• I₀ = intensity of plane polarised light
• I = intensity of transmitted light from the analyser
• θ = angle between the axis of the polariser and the analyser

Statement:

When unpolarised light is incident at polarising angle i_B on an interface separating air from a medium of refractive index μ, then the reflected light is plane polarised (perpendicular to the plane of incidence), provided:

Additional condition at polarising angle:

i.e., the reflected plane polarised light is at right angles to the refracted light.

OR

Statement:

• When the angle of incidence equals the polarising angle (θ_B), the reflected and refracted rays are perpendicular to each other.
• "The refractive index of a medium is equal to the tangent of the polarising angle θ_B."

It states that when a completely plane polarised light beam is incident on an analyzer, the intensity of the emergent light varies as the square of the cosine of the angle between the plane of transmission of the analyzer and the polarizer.

I = I₀cos²θ

• Diffraction = bending and spreading of light waves around obstacles or through narrow openings, producing interference patterns.
• It is due to interference of secondary wavelets from the exposed portion of the wavefront from the slit.
• Key difference from interference: in diffraction, bright fringes have same intensity but bands are of decreasing intensity.

Single Slit Diffraction:

Let a = width of slit, θ = angle of diffraction.

Condition for Minimum (Dark) Intensity:

Condition for Maximum (Secondary Bright) Intensity:

\[a\sin\theta=(2n+1)\frac{\lambda}{2},\quad n=1,2,3...\]

Width of Central Maximum:

For first minima: \[a\cdot\frac{y}{D}=\lambda\Rightarrow y=\frac{\lambda D}{a}\]

\[W=2y=\frac{2\lambda D}{a}\]

Angular width of central maximum:

Linear width of n-th secondary maximum: