Essential Physics Formulas and Numerical Problem Solving

Posted on May 11, 2026 in Secondary Education

1. Optics

Mirror and Lens Formulas

  • Mirror/Lens Formula: 1/f = 1/v + 1/u
  • Magnification: m = v/u = hi/ho
  • Power of Lens: P = 1/f (f in metres)
  • Combination of Lenses: Peq = P1 + P2 + …
  • Refractive Index: n = sin(i)/sin(r) = c/v
  • Critical Angle: sin C = 1/n

Numerical Tips

  • Always use sign conventions.
  • Convert focal length from cm to metres for power calculations.

2. Wave Optics

  • Fringe Width: β = (Dλ)/d
  • Bright Fringe Position: yn = nβ
  • Dark Fringe Position: yn = (2n – 1)β / 2
  • Diffraction Minimum: a sin θ = nλ
  • Resolving Power: Greater aperture = better resolution.

Numerical Tips

  • Use SI units for D, a, and d.
  • In YDSE, solve for fringe width first.

3. Photoelectric Effect

  • Einstein Equation: hv = φ + Kmax
  • Threshold Frequency: v0 = φ/h
  • Work Function: φ = hv0

Numerical Tips

  • If stopping potential (Vs) is given, Kmax = eVs.
  • Ensure units are consistent (eV or Joules).

4. de Broglie and Bohr Model

  • de Broglie Wavelength: λ = h/p = h/(mv)
  • Bohr Energy: En = -13.6/n² eV
  • Radius of Orbit: rn = (n²a0)/Z
  • Photon Energy: E = hv = hc/λ
  • Transition Energy: ΔE = E2 – E1

Numerical Tips

  • For hydrogen transitions, find |ΔE| first, then use λ = hc/ΔE.

5. Radioactivity and Nuclear Physics

  • Decay Law: N = N0e-λt
  • Half-life: T1/2 = 0.693/λ
  • Activity: A = λN
  • Mass-Energy Equivalence: Q = Δm × c² (1u = 931 MeV/c²)

Numerical Tips

  • For repeated half-life: N = N0(1/2)n.
  • Ensure t and T1/2 are in the same units.

6. Semiconductors and Electronics

  • Current Relation: IE = IB + IC
  • Current Gain (CE): β = α/(1 – α)
  • Rectifiers: Full-wave output is smoother than half-wave.
  • Zener Diode: Output remains constant in the reverse breakdown region.

7. Hall Effect

  • Hall Voltage: VH = BI/n e t
  • Applications: Identify semiconductor type, measure carrier concentration, and magnetic field sensing.

Numerical Tips

  • Use thickness (t) in metres.

8. Mini Solved Examples

  • SHM: Given A=0.15m, T=0.2s. ω = 2π/T = 31.4 rad/s. Vmax = ωA = 4.71 m/s.
  • Bernoulli: P1 + 0.5ρv1² = P2 + 0.5ρv2². Result: P2 = 1.34 × 10⁵ Pa.
  • Capacitor Energy: U = 0.5CV².
  • Magnetic Force: F = BIl sin θ.

9. Standard Result Box

  • AC Resonance: Impedance is minimum, current is maximum.
  • Photoelectric Effect: Intensity affects current, not stopping potential.
  • Radioactivity: Decay is independent of temperature and pressure.
  • Capacitors: Series combination decreases equivalent capacitance.
  • Resistors: Parallel combination decreases equivalent resistance.

10. Quick Final Checks

  • Write units in every answer.
  • Mention the formula name used.
  • Draw ray diagrams, energy levels, or circuit symbols where necessary.
  • Keep final answers neat and boxed.