OPTICS — ADVANCED:
  Young's Double Slit Experiment:
    Path difference: Δ = dsinθ ≈ dy/D
    Constructive: Δ = nλ | Destructive: Δ = (2n-1)λ/2
    Fringe width: β = λD/d
    Central maximum always bright regardless of source wavelength

  Single Slit Diffraction:
    First minimum: a sinθ = λ (slit width a)
    Central maximum width twice that of secondary maxima

  Thin Film Interference:
    Path difference = 2μt cosθ
    Phase change on reflection from denser medium (add λ/2)

WAVES — JEE ADVANCED LEVEL:
  Standing waves on string: λ = 2L/n (for nth harmonic, both ends fixed)
  Fundamental frequency: f = v/2L | v = √(T/μ) where μ = mass/length
  
  Organ pipes:
    Both ends open: f_n = nv/2L
    One end closed: f_n = (2n-1)v/4L (only odd harmonics)
  
  Doppler effect: f_observed = f_source × (v+v_observer)/(v-v_source)
    (+ when approaching, - when receding)

MODERN PHYSICS — ADVANCED:
  Binding energy: BE = [Zm_p + Nm_n - M(nucleus)] × 931.5 MeV/u
  Q-value of nuclear reaction: Q = (m_reactants - m_products) × 931.5 MeV/u
  
  X-rays: Bragg's law: 2d sinθ = nλ
  Photoelectric stopping potential: eV₀ = hf - φ (f_threshold = φ/h)

SYSTEMATIC APPROACH:
  1. Read problem carefully — identify what is given and what is asked
  2. Draw clear diagram (especially for optics, mechanics)
  3. Write all applicable physical principles/laws
  4. Set up equations (may be system of simultaneous equations)
  5. Solve algebraically first, substitute numbers at the end
  6. Check: units, signs, order of magnitude (sanity check)

COMMON ERRORS TO AVOID:
  Sign convention in optics: always define positive direction and stick to it
  Reference frame: clearly state which frame you are working in
  Initial and final conditions: for conservation laws (energy/momentum)
  Pseudo force: remember to add only in non-inertial frames
  Integration limits: be careful about direction of integration

MULTI-CONCEPT PROBLEMS (JEE Advanced style):
  Typically combine 2-3 chapters
  Example: rotating charged ring + electrostatics + rotational dynamics
  Approach: identify each concept separately, then combine