Micro Notes — Physics (compiled from provided sources) Summary & Study Notes

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1. Magnification (compound microscope): The total magnification is the product of objective and eyepiece magnifications: $M = M_o \times M_e$.

2. Refraction (Huygens’ principle): Huygens' principle: every point on a wavefront is a source of secondary wavelets; envelope gives new wavefront. Gives Snell's law: $n_1 \sin i = n_2 \sin r$.

3. Full-wave rectifier: Converts AC → pulsating DC using two diodes and a transformer; both halves of the input waveform are used.

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

5. Thin lenses in contact: Effective focal length of lenses in contact: $\dfrac{1}{F} = \dfrac{1}{f_1} + \dfrac{1}{f_2} + \dots$.

6. Refraction through a prism: Light refracts at both faces; angle of deviation $D$. At minimum deviation: $n = \dfrac{\sin\left(\dfrac{A + D}{2}\right)}{\sin\left(\dfrac{A}{2}\right)}$ where $A$ is prism angle.

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

8. Resonant frequency: Resonance when $X_L = X_C$. Resonant frequency: $f = \dfrac{1}{2\pi \sqrt{LC}}$; impedance is minimum, current maximal.

9. Transformer: Device transferring power between circuits by electromagnetic induction; used to step-up or step-down AC voltages.

10. Magnetic field inside a solenoid: For a long solenoid, field is approximately uniform: $B = \mu_0 n I$ where $n$ = turns per unit length.

11. Self-inductance of a solenoid: Self-inductance depends on geometry: $L = \mu_0 n^2 A l$ (with $n$ = turns per unit length, $A$ = cross-sectional area, $l$ = length).

12. AC generator: Rotating coil in a magnetic field induces an alternating emf by Faraday’s law; mechanical → electrical energy conversion.

13. Parallel-plate capacitor (capacitance): $C = \epsilon \dfrac{A}{d}$ where $A$ is plate area, $d$ is separation, and $\epsilon$ is permittivity of the medium.

14. Capacitors (series, parallel) & energy: Series: $\dfrac{1}{C} = \dfrac{1}{C_1} + \dfrac{1}{C_2} + \dots$; Parallel: $C = C_1 + C_2 + \dots$. Energy stored: $U = \dfrac{1}{2} C V^2$.

15. Wheatstone bridge: Used to measure unknown resistance. Balance condition: $\dfrac{P}{Q} = \dfrac{R}{S}$ (knowns P,Q,R; S unknown when balanced).

16. Kirchhoff’s laws: KCL: Sum of currents into a junction = sum out. KVL: Algebraic sum of voltages around a closed loop = 0.

17. Electric field on axial line of a dipole: For a point on the axis (far from dipole): $E = \dfrac{1}{4\pi \epsilon_0} \dfrac{2p}{r^3}$ where $p$ is dipole moment, $r$ is distance.

18. Gauss’s theorem (spherical shell): Outside a uniformly charged spherical shell, field acts as if charge concentrated at center: $E = \dfrac{1}{4\pi \epsilon_0} \dfrac{Q}{r^2}$. Inside a conducting shell the field is zero.

19. Uses of electromagnetic waves: Radio (communication), microwaves (radar, cooking), infrared (remote controls, heating), visible (vision), ultraviolet (sterilization), X-rays (medical imaging), gamma rays (cancer treatment).

20. Magnetic material types: Diamagnetic: weakly repelled (e.g., bismuth). Paramagnetic: weakly attracted (e.g., aluminium). Ferromagnetic: strongly attracted and retain magnetization (e.g., iron, cobalt, nickel).