Physics Micro Notes Summary & Study Notes

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Goal: Convert provided physics Q&A into concise micro notes. Short, focused paragraphs with bold key terms and formulas in LaTeX.

🧭 Format intent

You asked: "I want this Into micro notes" — the following section (from the PDF) is reformatted as compact study points, each emphasizing the main concept and the core formula where applicable.

🔬 Optics

Magnification (compound microscope): Product of objective and eyepiece magnifications: $M = M_o \times M_e$. Keep track of sign conventions for image orientation.

Refraction via Huygens’ principle: Every point on a wavefront emits secondary wavelets; the new wavefront is their envelope. Snell's law follows: $n_1 \sin i = n_2 \sin r$.

Lensmaker’s formula: Relates focal length to lens curvature and refractive index: $\displaystyle \frac{1}{f} = (n-1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$.

Thin lenses in contact: Effective focal length given by $\displaystyle \frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2} + \dots$.

Refraction through a prism (minimum deviation): Refractive index relation: $\displaystyle n = \frac{\sin\left(\dfrac{A+D}{2}\right)}{\sin\left(\dfrac{A}{2}\right)}$, where $A$ is prism angle and $D$ is minimum deviation.

⚡ Circuits & Electromagnetism

Full-wave rectifier: Uses diodes (and often a transformer) to convert both halves of an AC waveform into pulsating DC; more efficient than half-wave.

Series LCR circuit (AC): Impedance $Z = \sqrt{R^2 + (X_L - X_C)^2}$ with $X_L = \omega L$ and $X_C = \dfrac{1}{\omega C}$. Current: $I = \dfrac{V}{Z}$.

Resonant frequency (LCR): At resonance $X_L = X_C$ and impedance is minimum. Resonant frequency: $\displaystyle f = \frac{1}{2\pi\sqrt{LC}}$.

Transformer (basic): Transfers electrical energy between circuits via electromagnetic induction; used to step voltage up or down for AC.

Magnetic field inside a long solenoid: Uniform and approximately $B = \mu_0 n I$, where $n$ is turns per unit length and $I$ is current.

Self-inductance of a solenoid: For a solenoid $L = \mu_0 n^2 A l$ (with $n$ turns per unit length, $A$ cross-sectional area, $l$ length) — relates flux linkage to current.

AC generator (concept): Rotating coil in a magnetic field induces an alternating emf via Faraday's law; mechanical to electrical energy conversion.

⚙️ Capacitors, Wheatstone, Kirchhoff

Parallel-plate capacitor: $C = \varepsilon \dfrac{A}{d}$ (dielectric permittivity $\varepsilon$, plate area $A$, separation $d$).

Capacitors in series and parallel: Series: $\dfrac{1}{C} = \dfrac{1}{C_1} + \dfrac{1}{C_2} + \dots$. Parallel: $C = C_1 + C_2 + \dots$.

Energy stored in a capacitor: $U = \tfrac{1}{2} C V^2$.

Wheatstone bridge (balance): Used to find unknown resistance; balanced when $\dfrac{P}{Q} = \dfrac{R}{S}$.

Kirchhoff’s laws: Current law (KCL): sum of currents entering a node = sum leaving. Voltage law (KVL): algebraic sum of voltages around closed loop = 0.

🔌 Electrostatics & Gauss

Electric field on axial line of a dipole: For distance $r$ from center on axis, $E = \dfrac{1}{4\pi\varepsilon}\dfrac{2p}{r^3}$, where $p$ is dipole moment.

Gauss’s theorem for a spherical shell: Outside the shell the field is as if charge concentrated at center: $E = \dfrac{1}{4\pi\varepsilon}\dfrac{Q}{r^2}$. Inside a uniformly charged spherical shell $E = 0$.

📡 Electromagnetic waves & Applications

Uses of EM spectrum: Radio — communication; Microwaves — radar and cooking; Infrared — remote controls, heating; Visible — vision; Ultraviolet — sterilization; X-rays — imaging; Gamma rays — cancer treatment.

🧲 Magnetic materials

Diamagnetic: Weakly repelled by magnetic fields (e.g., bismuth).

Paramagnetic: Weakly attracted (e.g., aluminium).

Ferromagnetic: Strongly attracted and can retain magnetization (e.g., iron, cobalt, nickel).