Electromagnetic Waves and Phenomena
Electromagnetic Waves
Electromagnetic waves are horizontal and involve the propagation of electric and magnetic fields perpendicular to the direction of propagation, without requiring a material medium.
Characteristics of Electromagnetic Waves
- Caused by accelerated electric charges.
- Consist of periodic variations of the electromagnetic state of space.
- Do not need material support to propagate.
- Electric and magnetic field vectors vary sinusoidally with time and position, following equations for harmonic waves.
- The ratio of the magnitudes of the electric field (E) and magnetic field (B) at a given position and time is equal to the speed of light (c): E/B = c.
- The speed of electromagnetic waves depends on the propagation medium.
- The relationship between speed (c), wavelength (λ), and frequency (f) is: λ = c/f.
Electromagnetic Spectrum
The electromagnetic spectrum is the ordered sequence of all known electromagnetic waves, arranged by wavelength or frequency.
Groups of Waves in the Spectrum
Gamma rays, X-rays, ultraviolet, visible light, infrared, microwave, shortwave radio, TV and FM radio waves, AM radio waves, and longwave radio waves.
Rectilinear Propagation of Light
A ray of light is a line perpendicular to the wave surface and indicates the direction of propagation.
Shadow
When a point source illuminates an opaque object, a non-illuminated region or shadow appears behind it, reproducing the object’s contour defined by the tangent rays.
Penumbra
When a finite-sized light source illuminates an opaque object, a partially illuminated area called the penumbra appears around the shadow.
Eclipses
Eclipse of the Sun
A solar eclipse occurs when the Moon blocks the Sun from a specific location on Earth. This can only happen during a new moon (Sun and Moon in conjunction). The Moon’s shadow creates total and partial solar eclipses. The eclipse is total for areas within the umbra and partial for areas within the penumbra.
Lunar Eclipse
A lunar eclipse occurs when the Earth passes between the Sun and the Moon, causing the Moon to enter the Earth’s shadow. This can only occur during a full moon.
Velocity of Propagation
Fizeau’s Method
Fizeau’s method measures the speed of light. A light beam is passed between two consecutive teeth of a rotating cogwheel. The beam reflects off a distant mirror and returns along the same path. At low rotation speeds, the reflected light is blocked by the teeth. To determine the speed of light, the angular velocity of the cogwheel must be known so that the reflected light passes through the next opening. Knowing the angular velocity (25.2 rev/s), the time it takes for the light to travel to the mirror and back is calculated. The obtained value is slightly higher than the actual value.
Diffraction
Diffraction is the deviation from rectilinear propagation when waves pass through an opening or near an obstacle. It is a characteristic property of waves.
Reflection
Reflection occurs when a wave reaches the surface separating two media and returns to the first medium with part of its energy, changing its direction of propagation.
Laws of Reflection
- The incident ray, the normal to the surface at the point of incidence, and the reflected ray lie in the same plane.
- The angle of incidence (i) equals the angle of reflection (r).
Refraction
Refraction occurs when a wave reaches the surface between two media and enters the second medium with part of its energy, changing its direction of propagation.
Laws of Refraction
- The refracted ray, the normal, and the incident ray lie in the same plane.
- The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant and equal to the ratio of the wave speeds in the two media. This constant is the refractive index of the second medium relative to the first (n₂₁).
Snell’s Law
The product of the refractive index and the sine of the angle of incidence is constant for any light ray incident on the interface between two media. Snell’s law applies to all types of waves.
Critical Angle
The critical angle is the angle of incidence that corresponds to an angle of refraction of 90 degrees.
Dispersion
Dispersion occurs when a light beam is refracted in a composite medium (e.g., a prism) and separates into its constituent colors. The refractive index decreases with increasing wavelength, causing longer wavelengths to be deflected less than shorter ones.
Optical Prism
An optical prism is a system of two refracting surfaces forming a dihedral angle called the prism angle.
Spectrum of White Light
Different wavelengths of white light refract at different angles, emerging and appearing as a continuous series of colors on a screen.
Rainbow
A rainbow is formed by the dispersion of sunlight due to refraction within water droplets suspended in the air after rain. The observer must have the sun behind them.
Primary Rainbow
Colors range from violet to red, following the spectrum of white light. Light is reflected inside the droplets and refracted at entry and exit. Red light undergoes the greatest deviation. The observer sees violet drops lower on the horizon and red drops higher.
Secondary Rainbow
Formed by double reflection inside the droplets, with colors inverted compared to the primary rainbow.
Spectroscopy
Spectroscopy examines and interprets radiation spectra obtained with a spectroscope. Spectroscopes measure light properties within specific portions of the electromagnetic spectrum. Continuous spectra resemble white light, while discontinuous spectra show brightly colored lines at different wavelengths and frequencies. Emission spectra analyze light emitted by a chemical, while absorption spectra study light after passing through a compound that absorbs some components.
Wave Interference
Wave interference is the superposition of two or more wave motions at a point.
Principle of Superposition
Interference phenomena are governed by the principle of superposition, which states that the resultant vibration at a point where two waves meet is the sum of the vibrations each wave would produce individually.
Types of Interference
Constructive Interference
Resultant amplitude is greater than the individual wave amplitudes. In the case of coherent sources (f₁ = f₂), the path difference is X₁P – X₂P = nλ (n = 1, 2, …), the phase difference is φ = 2nπ, and the resultant amplitude is Aᵣ = A₁ + A₂.
Destructive Interference
Resultant amplitude is less than the individual wave amplitudes. For coherent sources, the path difference is X₁P – X₂P = (2n + 1)λ/2 (n = 1, 2, …), the phase difference is φ = (2n + 1)π, and if A₁ = A₂, then Aᵣ = 0.
Young’s Double-Slit Experiment
Young’s double-slit experiment demonstrates light interference. Monochromatic light illuminates a screen with two slits, which act as coherent sources. The waves interfere, creating an interference pattern on another screen with bright and dark fringes. Bright fringes result from constructive interference, while dark fringes result from destructive interference.