Electromagnetic Waves

Speed of Electromagnetic Waves

Electromagnetic (EM) waves consist of oscillating electric and magnetic fields that propagate through space. The speed of these waves in a vacuum is a fundamental constant of nature.

• Simple EM Wave: Consider an electric field in the y-direction and a magnetic field in the z-direction, propagating in the x-direction with speed c.

• Relationship between Fields: The electric and magnetic fields satisfy Maxwell's equations only if:

• Speed of Light: The speed of light in vacuum is given by:

• Key Point: Light is an electromagnetic wave.

General Properties of Electromagnetic Waves

All electromagnetic waves share several important properties, regardless of their specific form.

• Transverse Nature: The electric field (E) and magnetic field (B) are perpendicular to each other and to the direction of propagation.

• Fixed Ratio: The magnitudes of the fields are related by:

• Constant Speed: In vacuum, all EM waves travel at .

• No Medium Required: EM waves can propagate through a vacuum (unlike sound waves).

• Right-Hand Rule: The direction of B relative to E and the direction of propagation can be determined using the right-hand rule.

Sinusoidal Waves

Sinusoidal waves are a fundamental type of wave whose time and space dependence follow a sine function.

• Snapshot: At any instant, the electric and magnetic fields oscillate sinusoidally and are perpendicular to each other and to the direction of propagation.

• Right-Hand Rule: Used to determine the orientation of the fields.

The Electromagnetic Spectrum

Wavelength, Frequency, and the Spectrum

Electromagnetic waves are characterized by their wavelength () and frequency (), which are related by:

• Classification: Different ranges of wavelength and frequency correspond to different types of EM waves (radio, microwave, infrared, visible, ultraviolet, X-rays, gamma rays).

Visible Light: The visible spectrum ranges from about 400 nm (violet) to 700 nm (red).

Wave Fronts and Rays

Wave Fronts

A wave front is a surface on which the phase of a wave is constant (i.e., all points are at the same stage of vibration).

• Plane Wave: All points on a plane perpendicular to the direction of propagation are in phase.

Rays and Wave Fronts

Rays are imaginary lines drawn perpendicular to wave fronts, indicating the direction of energy propagation.

• Planar Wave Fronts: Rays are parallel and perpendicular to the wave fronts.

• Spherical Wave Fronts: Rays radiate outward from a point source, perpendicular to the spherical wave fronts.

• Application: Rays are useful for geometric optics, such as tracing the path of light through lenses and mirrors.

Describing Light by Rays

Light can be described by rays, especially when considering how it interacts with surfaces.

• Scattering: Non-luminous objects are visible because they scatter incident light in many directions.

• Rough Surfaces: Scatter light in many directions (diffuse reflection).

• Smooth Surfaces: Reflect light in a single direction (specular reflection).

• Example: Reading a page involves seeing light scattered from the paper's surface.

Reflection and Refraction

Reflection of Light

When light encounters a boundary between two media, some of it may be reflected.

• Law of Reflection: The angle of incidence equals the angle of reflection:

Refractive Index

Light travels slower in materials than in vacuum due to interactions with atoms. The refractive index quantifies this effect.

• Definition: The refractive index n is the ratio of the speed of light in vacuum to that in the material:

,  

• Optical Properties: The refractive index determines how much light bends when entering a material.

Refraction of Light

Refraction is the bending of light as it passes from one medium to another with a different refractive index. The angle of refraction is determined by Snell's Law:

• Increasing n: Light bends toward the normal (slower medium).

• Decreasing n: Light bends away from the normal (faster medium).

Total Internal Reflection

Total internal reflection occurs when light attempts to move from a medium with higher refractive index to one with lower refractive index at a sufficiently large angle.

• Critical Angle: When the angle of incidence exceeds the critical angle, all light is reflected back into the original medium.

Wave Speed, Frequency, and Wavelength in Materials

When light enters a material, its speed decreases, but its frequency remains constant. The wavelength changes according to:

• In Vacuum: ,

• In Material: ,

• Frequency: (remains unchanged)

Key Point: The decrease in speed inside a material results in a shorter wavelength, but the frequency of light does not change.

Summary Table: Light Properties in Different Media

Example: If light of wavelength 600 nm in vacuum enters glass with , its wavelength in glass is , but its frequency remains unchanged.

Additional info: These notes cover the core concepts of electromagnetic waves, their propagation, and the basics of geometric optics, as outlined in standard college physics curricula.