JEE Physics Notes: Wave Optics

Introduction to Wave Optics

Wave optics, also known as physical optics, deals with the wave nature of light. It explains phenomena such as interference, diffraction, and polarization, which cannot be explained using ray optics.

Huygens’ Principle

Huygens’ principle states that every point on a wavefront acts as a secondary source of wavelets, which spread out in all directions. The new wavefront is obtained by drawing a tangent to all secondary wavelets.

Wavefront and Types

• Spherical wavefront: Formed by a point source.
• Cylindrical wavefront: Produced by a linear source.
• Plane wavefront: Formed at a large distance from the source.

Interference of Light

Interference is the superposition of two or more waves leading to a resultant intensity distribution. It can be constructive or destructive.

Conditions for Interference

• The sources must be coherent (same frequency and constant phase difference).
• The sources must have nearly the same amplitude.
• The superposition should occur in the same medium.

Young’s Double Slit Experiment (YDSE)

Young’s double-slit experiment demonstrates the interference of light waves.

The fringe width is given by:

β = (λD) / d

where:

• λ = wavelength of light
• D = distance between slits and screen
• d = distance between the two slits

Diffraction of Light

Diffraction is the bending of light waves around obstacles and the spreading of waves when they pass through small openings.

Types of Diffraction

• Fresnel Diffraction: Occurs when the source or screen is at a finite distance.
• Fraunhofer Diffraction: Occurs when the source and screen are at an infinite distance.

Single-Slit Diffraction

For a single slit of width a, the first minimum occurs at:

a sinθ = mλ,  (m = ±1, ±2, ±3,...)

The central maximum is the brightest and widest.

Polarization of Light

Polarization is the phenomenon where light waves oscillate in a single plane. It occurs only for transverse waves.

Types of Polarization

• Plane polarization: Light vibrates in only one plane.
• Circular polarization: The electric field rotates in a helical pattern.
• Elliptical polarization: A general case of circular and linear polarization.

Malus’ Law

Malus’ Law states that the intensity of polarized light transmitted through an analyzer is given by:

I = I₀ cos²θ

where θ is the angle between the light's initial polarization direction and the analyzer’s axis.

Applications of Wave Optics

• Anti-reflective coatings
• Optical instruments such as microscopes and telescopes
• Holography
• Polarized sunglasses and LCD screens

Wave optics is essential for understanding the nature of light and solving JEE Physics problems related to interference, diffraction, and polarization.