Comprehensive Guide to Properties of Waves and Physical Optics

Electromagnetic (EM) radiation

Consists of oscillating electric and magnetic fields that propagate through space.

Transverse Waves

Waves whose oscillations are perpendicular to the direction of wave propagation.

Speed of Light (c)

All EM waves travel at this speed in a vacuum: c = 3.00 × 10^8 m/s.

Wave Equation

The relationship between speed (v), frequency (f), and wavelength (λ): v = fλ.

Energy of EM Waves

Energy is directly proportional to frequency: E = hf.

Electromagnetic Spectrum

A range of EM radiation categorized by wavelength or frequency, including Radio Waves, Microwaves, Infrared, Visible Light, Ultraviolet, X-Rays, and Gamma Rays.

Index of Refraction (n)

Defined as n = c/v, where c is the speed of light in vacuum and v is the speed in the medium.

Superposition Principle

When two waves overlap, the resulting amplitude is the algebraic sum of the individual amplitudes.

Constructive Interference

Occurs when crest meets crest (or trough meets trough), resulting in increased amplitude.

Destructive Interference

Occurs when crest meets trough, resulting in decreased amplitude or cancellation.

Path Length Difference (ΔL)

The difference in distance traveled by two waves arriving at a point.

Condition for Constructive Interference (Maxima)

ΔL = mλ, where m = 0, 1, 2,… (the difference is a whole number of wavelengths).

Condition for Destructive Interference (Minima)

ΔL = (m + 1/2)λ, where m = 0, 1, 2,… (the difference is a half-integer of wavelengths).

Young's Double-Slit Experiment

An experiment demonstrating that light behaves as a wave, producing a pattern of bright and dark fringes.

Path Difference Geometry

ΔL = d sin(θ), where d is the distance between the slits and θ is the angle from the center line.

Location of Bright Fringes (Maxima)

d sin(θ) = mλ, where m is an integer.

Location of Dark Fringes (Minima)

d sin(θ) = (m + 1/2)λ, where m is an integer.

Small Angle Approximation

If L >> d, then sin(θ) ≈ tan(θ) ≈ y/L.

Fringe spacing (y) relation

y_m ≈ (m λ L) / d, showing spacing between fringes is influenced by wavelength, slit separation, and screen distance.

Diffraction Gratings

Devices with many slits that produce sharper and brighter maxima.

Single Slit Diffraction

Interference caused by a single opening, producing a wider central maximum and dark spots.

Minima formula for Single Slit

a sin(θ) = mλ, where a is the width of the slit and m is an integer for dark spots.

Thin Film Interference

Interference resulting from light waves reflecting off the top and bottom surfaces of a thin film.

Phase Shift for Hard Reflection

A 180° phase shift occurs when light reflects off a denser medium.

Phase Shift for Soft Reflection

No phase shift occurs when light reflects off a less dense medium.

Path length in Thin Films

Relative path length is 2t, where t is the thickness of the film.

Constructive Interference for Thin Films (No Phase Shift)

2t = mλfilm, where λfilm is the wavelength inside the film.

Destructive Interference for Thin Films (No Phase Shift)

2t = (m + 1/2)λ_film.

Elastic Reflection (Phase Shift)

One phase shift when one side of the film reflects off a denser medium.

Malus' Law

Describes how polarized light intensity changes when passing through a polarizer at angle θ: I = I_0 cos²(θ).

Polarized Light

Light with electric field oscillations in a specific direction.

Unpolarized Light

Light in which the electric field oscillates in random directions.

Slit Width (a)

The width of the gap in a single slit diffraction setup.

Slit Separation (d)

The distance between the centers of slits in a double slit experiment.

Small Angle Condition

y = mλL/d is applicable only for small angles; otherwise use d sin(θ) = mλ.

Frequency in Media Change

When light enters a medium, frequency remains constant while speed and wavelength change.

Constructive vs Destructive Conditions

In double slit, m gives bright spots; in single slit, m gives dark spots.

Crucial Step in Thin Films

Always calculate λfilm using λvacuum/n_film.

Phase Shifts Count

Count phase shifts in reflection to determine formula for interference.

Differences Between Interference Types

Single slit produces dark spots while double slit produces bright spots for integer m.

Energy-Frequency Relationship

Higher frequency results in higher energy for EM waves.

Electromagnetic Spectrum Order

The order by wavelength from longest to shortest: Radio, Microwave, Infrared, Visible Light, Ultraviolet, X-Rays, Gamma Rays.

Constructive Condition for Thin Films

When there are 0 or 2 phase shifts, use 2t = mλ_film.

Destructive Condition for Thin Films with Phase Shift

For 1 phase shift, use 2t = (m + 1/2)λ_film.

Malus' Law for Polarizers

Intensity I after passing through a polarizer is I = I_0 cos²(θ).