Physics Formulas and Concepts

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1. Sound Waves Oscillation: Periodic motion about an equilibrium position. Amplitude ($a$): Maximum displacement from equilibrium. SI unit: meter (m). Period ($T$): Time for one oscillation. SI unit: second (s). Frequency ($f$): Number of oscillations per second. SI unit: Hertz (Hz). Relation between Period and Frequency: $f = \frac{1}{T}$ Natural Frequency: Inherent frequency of free vibration. Forced Vibration: Vibration induced by an external force. Resonance: Maximum amplitude vibration when forcing frequency equals natural frequency. Wave Motion: Propagation of energy without net particle displacement. Mechanical Waves: Require a medium (e.g., sound). Electromagnetic Waves: Do not require a medium (e.g., light). Longitudinal Waves: Particles vibrate parallel to wave propagation (e.g., sound). Transverse Waves: Particles vibrate perpendicular to wave propagation (e.g., light). Wavelength ($\lambda$): Distance between two consecutive particles in the same phase. SI unit: meter (m). Speed of Wave ($v$): Distance traveled by the wave in one second. SI unit: m/s. Wave Equation: $v = f \lambda$ Reflection of Sound: Sound waves bouncing off surfaces. Echo: Distinct reflected sound heard after a time delay. Persistence of Hearing: Auditory sensation lasts for $\approx 0.1$ s. Minimum distance for echo: For distinct echo, $d \ge \frac{v \times 0.1 \text{ s}}{2}$. For $v = 350$ m/s, $d \approx 17.5$ m. Reverberation: Lingering of sound due to multiple reflections. Limits of Audibility: Human audible range: $20$ Hz to $20000$ Hz. Infrasonic: $ Ultrasonic: $> 20000$ Hz. Uses of Ultrasonic Waves: Medical imaging (sonography), cleaning, SONAR, industrial applications. 2. Lenses Lens: Transparent medium with two refracting surfaces. Convex Lens (Converging): Thicker at center, converges light. Concave Lens (Diverging): Thinner at center, diverges light. Optic Centre (O): Geometric center of the lens. Principal Focus (F): Convex: Point where parallel rays converge. Concave: Point from which parallel rays appear to diverge. Focal Length ($f$): Distance from optic centre to principal focus. Image Formation - Convex Lens: Object beyond $2F$: Image between $F$ and $2F$, diminished, inverted, real. Object at $2F$: Image at $2F$, same size, inverted, real. Object between $F$ and $2F$: Image beyond $2F$, magnified, inverted, real. Object at $F$: Image at infinity, highly magnified, inverted, real. Object between $F$ and O: Image on same side, magnified, erect, virtual. Image Formation - Concave Lens: Always diminished, erect, virtual, between F and O on the same side. Cartesian Sign Convention: Distances from optic centre. Incident light direction: positive. Above principal axis: positive. Lens Equation: $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ (or $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$) Magnification ($m$): $m = \frac{\text{Height of image }(h_i)}{\text{Height of object }(h_o)} = \frac{\text{Image distance }(v)}{\text{Object distance }(u)}$ Power of Lens ($P$): $P = \frac{1}{f \text{ (in meters)}}$ SI unit for Power: Dioptre (D). $1 \text{ D} = 1 \text{ m}^{-1}$. Convex lens: Positive power. Concave lens: Negative power. 3. The World of Colours and Vision Refraction through a Prism: Light bends towards the base. Dispersion of Light: Splitting of white light into its constituent colors (spectrum). VIBGYOR: Violet (shortest $\lambda$, most deviation) to Red (longest $\lambda$, least deviation). Rainbow: Formed by dispersion, refraction, and internal reflection in water droplets. Electromagnetic Spectrum: Range of EM radiation (radio, micro, IR, visible, UV, X-ray, gamma). Primary Colours of Light: Red, Green, Blue (RGB). Mixing them produces white light. Secondary Colours of Light: Red + Green = Yellow Red + Blue = Magenta Green + Blue = Cyan Complementary Colours: A primary and a secondary color that combine to produce white light (e.g., Yellow + Blue). Persistence of Vision: Image remains on retina for $\approx \frac{1}{16}$ s. Colour of Objects: Transparent: Transmits its own color. Opaque: Reflects its own color. Scattering of Light: Shorter wavelengths (blue) scatter more than longer wavelengths (red). Explains blue sky and red sunsets. Tyndall Effect: Scattering of light by colloidal particles, making the light path visible. Eye and Vision: Power of Accommodation: Eye's ability to change focal length. Near Point: Closest clear vision (approx. $25$ cm). Far Point: Farthest clear vision (infinity). Myopia (Short-sightedness): Image in front of retina. Corrected with concave lens. Hypermetropia (Long-sightedness): Image behind retina. Corrected with convex lens. Presbyopia: Age-related loss of accommodation. 4. Magnetic Effect of Electric Current Magnetic Field: Region around a magnet where its force is felt. Oersted's Discovery: Electric current creates a magnetic field. Right Hand Thumb Rule (for straight conductor): Thumb in current direction, fingers curl in magnetic field direction. Magnetic Field of a Solenoid: Behaves like a bar magnet when current flows. Strength $\propto$ Number of turns per unit length, Current, Nature of core material. Right Hand Rule for Solenoid: Fingers curl in current direction, thumb points to North pole. Electromagnets: Temporary magnets created by current. Motor Principle: A current-carrying conductor in a magnetic field experiences a force. Fleming's Left Hand Rule: Thumb: Direction of Force (Motion) Forefinger: Direction of Magnetic Field (N to S) Middle Finger: Direction of Current Electric Motor: Converts electrical energy to mechanical energy. Principle: Motor principle. Commutator (Split Rings): Reverses current direction in coil every half rotation for continuous motion. Moving Coil Loudspeaker: Converts electrical signals to sound. Voice coil in magnetic field experiences force (motor principle), causing vibration and sound production.