Wave Properties and Reflection

Wave Properties

• Amplitude (A): Maximum displacement from the original position, measured in meters.
• Wavelength (λ): Horizontal distance between two points in phase, measured in meters.
• Period (T): Time for a wave to complete one cycle, measured in seconds.
• Frequency (f): Number of cycles per second, measured in Hertz (Hz).
• Relationship between Frequency and Period: f = 1/T
• Wave Speed (v): Calculated as v = fλ (speed in m/s, frequency in Hz, wavelength in meters).
• Transverse Waves: Particles vibrate perpendicular to the wave's direction of motion. Examples include electromagnetic waves, water waves, and S-seismic waves.
• Longitudinal Waves: Particles vibrate parallel to the wave's direction of motion. Examples include sound waves and P-seismic waves.
• Wave Phenomena: Waves exhibit reflection, refraction, and diffraction.

Reflection

• Reflection: Change in direction when a wave collides with a reflective barrier. The angle of incidence equals the angle of reflection.

Refraction

• Refraction: Change in direction when a wave passes through a different medium.
• Refraction and Medium Changes: Refraction occurs when the wave direction isn't perpendicular to the medium boundary. The speed of the wave changes with the medium (e.g., water depth).
• Deep to Shallow Water: Wave speed decreases and wavelength shortens.
• Shallow to Deep Water: Wave speed increases and wavelength lengthens.

Diffraction

• Diffraction: Spreading of a wave as it passes through an opening or around an edge.
• Factors Affecting Diffraction: Diffraction increases with smaller gaps or larger wavelengths.

Light as a Wave

• Light exhibits reflection, refraction, and diffraction; hence it is a wave.

Reflection in a Plane Mirror

• Image Characteristics: Upright, virtual, laterally inverted, and same size as the object.
• Image Formation: Same distance from the mirror as the object.

Refraction of Light

• Refraction: Bending of light rays at the boundary of two media with different densities
• Denser Medium (i > r): When light passes from a less dense medium to a denser medium, the angle of incidence is greater than the angle of refraction.
• Less Dense Medium (i < r): When light passes from a denser medium to a less dense medium, the angle of incidence is less than the angle of refraction.
• Snell's Law: (sin i) / (sin r) = constant (n); where n is the refractive index, which is constant for a specific medium and light. n > 1.
• Refractive Index: Ratio of the speeds of a wave in two different regions. Another formula for refractive index is

Total Internal Reflection

• Total Internal Reflection: Occurs when a light ray propagates from an optically denser to a less dense medium and the angle of incidence is greater than the critical angle (Note: Light ray begins from optically denser medium and incident/reflects/refracts at a boundary to a less dense medium. The angle must exceed the critical angle.). This results in complete reflection.

• Critical Angle: Angle where a light ray reflects internally completely instead of passing into another medium.

• Phenomena related to Total Internal Reflection & Critical Angle:

  • Mirage
  • Rainbow

Thin Lenses

• Converging Lenses (Convex): Parallel light rays focus at a single point (principal focus, f) and produce real or virtual images.
• Diverging Lenses (Concave): Parallel light rays diverge; the image is always virtual.
• Ray Diagrams: Essential for analyzing image characteristics (real/virtual, enlarged/diminished, upright/inverted). Use three specific rules.
• Focal Length (f): Distance from the lens to the principal focus (depends on the curvature of the lens).
• Principal Axis: Imaginary line passing through the center of the lens.
• Principal Focus (Focal Point): Point where parallel light rays converge or appear to diverge.

Dispersion of Light

• Dispersion: Separation of white light into its constituent colours by refraction, based on varying degrees of bending for each colour.
• Spectrum: Sequence of colours (red, orange, yellow, green, blue, indigo, violet) in order of decreasing wavelength (or increasing frequency).
• Monochromatic Light: Light of a single frequency/wavelength.

Electromagnetic Spectrum

• Electromagnetic Waves: Transverse waves consisting of electric and magnetic fields; travel at the speed of light in a vacuum (3 x 10⁸ m/s).
• Frequency & Wavelength: Frequency increases and wavelength decreases as you move from radio waves to gamma rays.
• Applications: Various regions of the spectrum have specific applications (radio, microwave, infrared, visible, ultraviolet, X-ray, gamma ray).
• Harmful Effects of Excessive Exposure: Different parts of the electromagnetic spectrum can cause various health issues (e.g., microwaves causing internal heating).

Sound Waves

• Sound Waves: Longitudinal waves requiring a medium to propagate.
• Speed of Sound: Fastest in solids, then liquids, then gases.
• Frequency & Pitch: Higher frequency correlates to a higher pitch.
• Amplitude & Loudness: Higher amplitude correlates to a louder sound.
• Human Hearing Range: 20 Hz to 20 kHz.
• Ultrasound: Sound waves with frequencies above 20 kHz.
• Applications: Non-destructive testing, medical scanning, sonar.
• Echo: Reflection of a sound wave.