Electromagnetic Waves and Their Properties

Electromagnetic Waves

Electromagnetic waves are transverse because their electric and magnetic fields oscillate perpendicular to the direction of wave propagation.

Speed of Electromagnetic Waves

In a vacuum, electromagnetic waves travel at c = 3 × 10^8 m/s. In other media, their speed decreases due to interactions with atoms, but their frequency remains constant.

Medium Requirement

Electromagnetic waves do not require a medium because they consist of oscillating electric and magnetic fields. Sound waves are mechanical waves that rely on particle vibrations in a medium.

Wave Speed Calculation

A wave has a frequency of 50 Hz and a wavelength of 2 m. v = fλ = 50 × 2 = 100 m/s.

Frequency from Period

If the period of a wave is 0.02 s, its frequency is f = 1/T = 1/0.02 = 50 Hz.

Wavelength and Frequency Relationship

Wavelength is inversely proportional to frequency (λ = v/f), so doubling the frequency halves the wavelength.

Frequency Calculation in Air

A wave travels at 340 m/s in air. If its wavelength is 17 m, its frequency is f = v/λ = 340/17 = 20 Hz.

Electromagnetic Spectrum Order

The regions of the electromagnetic spectrum in order of increasing energy are: Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays.

Harmful Effects of UV Radiation

UV radiation can damage skin cells, leading to sunburn, premature aging, and an increased risk of skin cancer.

Microwaves vs Visible Light

Microwaves have longer wavelengths (1 mm to 1 m) compared to visible light (400-700 nm). Visible light has higher energy because energy increases with frequency (E = hf).

Uses of Gamma Rays in Medicine

Gamma rays are used in radiation therapy to kill cancer cells and sterilize medical equipment.

Refraction Calculation

Light travels from air (n = 1) into glass (n = 1.5). If the angle of incidence is 30°, using Snell's Law, θ2 = sin⁻¹(0.333) ≈ 19.5°.

Critical Angle Calculation

For light travelling from water (n = 1.33) to air (n = 1), the critical angle θc = sin⁻¹(0.75) ≈ 48.6°.

Prism and Spectrum

A prism splits white light into a spectrum of colours.

Dispersion

Different wavelengths of light refract at different angles as they pass through the prism, causing dispersion.

Refractive Index

The refractive index (n) is inversely proportional to the speed of light in the medium (v = c/n).

Temperature Conversion

0 K = −273.15 °C.

Thermal Energy Increase

Heating increases the kinetic energy of particles (they move faster) and their potential energy (interatomic forces change).

Conduction vs Convection

In conduction, particles vibrate but do not move from their positions. In convection, particles move from one place to another, carrying heat with them.

Evaporation Cooling

Evaporation removes the highest-energy molecules from the liquid, reducing the average kinetic energy (temperature) of the remaining molecules.

Energy Calculation for Heating Water

Q = mcΔT = 2 × 4200 × (80 − 20) = 504,000 J.

Energy to Melt Ice

Q = mL = 0.5 × 334,000 = 167,000 J.

Specific Heat Capacity Calculation

If 2000 J of energy is added to 0.1 kg of a substance, and its temperature increases by 10°C, what is its specific heat capacity?

Wien's Law Peak Wavelength

λmax = bT = 2.898 × 10−3 / 6000 = 4.83 × 10−7 m (483 nm, visible light).

Energy Emission Comparison

Energy is proportional to T^4, so the object at 600 K emits 16 times more energy than the object at 300 K.

Wien's Law and Wavelength

According to Wien's Law, λmax is inversely proportional to temperature. Hotter objects have more energy, leading to higher-frequency (shorter wavelength) radiation.

Optical Fibres in Endoscopy

Optical fibres transmit light into the body, allowing doctors to see internal organs without invasive surgery.

Microwaves in Communication

Microwaves can penetrate the atmosphere and travel long distances without significant signal loss.

X-ray Production and Use

X-rays are produced by high-energy electron collisions. They penetrate soft tissues but are absorbed by dense materials like bones, creating contrast in images.

Greenhouse Effect and Infrared Radiation

Greenhouse gases absorb and re-emit infrared radiation from the Earth's surface, trapping heat and warming the atmosphere.

Kelvin Scale in Science

The Kelvin scale starts at absolute zero (0 K), where all molecular motion stops, making it ideal for thermodynamic calculations.