Optics & Modern Physics · 100% marks notes

Method 01 · Sign convention stamp

One stamp prevents mid-solution sign drift — the #1 Advanced optics failure.

Do this: Write ‘Cartesian: incident direction +’ (or your school’s rule) on the figure before assigning u.

Method 02 · Sequential imaging

Turns ‘hard’ systems into repeated single-element solves.

Do this: For combinations, finish optic 1 completely (v₁, nature), shift origin to optic 2, redefine u₂.

Method 03 · TIR inequality first

Many MC options hinge only on whether TIR occurs.

Do this: Check i ≷ i_c before computing messy refraction angles.

Method 04 · Magnification product

Orientation follows sign of product without re-deriving.

Do this: m_total = m₁ m₂ … with each m using that element’s u,v.

Mirror / thin-lens formula

Looks like: u–v–f with sign convention

Fast model: State sign convention once; 1/v−1/u=1/f (lens) or mirror form.

Combination of lenses/mirrors

Looks like: Two thin lenses, silvered lens, or mirror+lens

Fast model: Image of first is object for second; track intermediate.

Refraction at spherical surface / TIR

Looks like: μ₁/u + … ; critical angle

Fast model: Use refraction formula; TIR when i>i_c=sin⁻¹(μ₂/μ₁).

Prism deviation and dispersion

Looks like: δ=(μ−1)A; angular dispersion

Fast model: Minimum deviation relates μ to A and δ_m.

Method 01 · Path-difference first

One Δ drives position, order and I; skipping it causes off-by-half-fringe errors.

Do this: Compute Δ before writing bright/dark or intensity.

Method 02 · YDSE-only gate

Respects syllabus limit; prevents false ‘interference’ templates.

Do this: If stem is Newton rings, thin film, grating multi-line interference — mark out of official interference scope for this notes track.

Method 03 · Diffraction vs interference label

Stops mixing a and d in the same formula.

Do this: Single-slit uses aperture a and mλ minima; YDSE uses slit separation d and β=λD/d.

Method 04 · Polarisation chain

Multiple Polaroids are sequential cos² factors, not one angle guess.

Do this: Track E-axis through each Polaroid; apply Malus at each analyser step.

YDSE fringe pattern

Looks like: β=λD/d; path difference d sinθ

Fast model: Path difference → phase → intensity I=4I₀ cos²(φ/2).

Optical-path insertion

Looks like: Thin film/slab in one YDSE path

Fast model: Extra OPD = (μ−1)t shifts fringes by ΔN=OPD/λ.

Single-slit diffraction

Looks like: Minima a sinθ=mλ; width of central max

Fast model: Central bright half-width ∼λ/a; secondary minima at mλ.

Polarisation / Brewster

Looks like: Malus I=I₀ cos²θ; μ=tan i_p

Fast model: Brewster: reflected ray ⊥ refracted; μ=tan i_p.

Method 01 · Einstein line first

Slope h/e, intercept ν₀, and intensity myths become obvious.

Do this: Always write hν=φ+K_max before reading a V_0–ν graph.

Method 02 · Unit bridge

Stops φ in eV mixed with h in J·s mid-line.

Do this: Convert everything to eV or everything to J once; use hc=12400 eV·Å when handy.

Method 03 · Transition difference

Kills ‘wavelength of n=2 orbit’ distractors.

Do this: Photon energy is |E_i−E_f|, never a single level’s E_n alone.

Method 04 · Z-scaling ratios

Ratio questions finish without Rydberg constants.

Do this: For H-like comparisons, factor Z² out of energies and 1/Z out of radii before numbers.

Einstein photoelectric equation

Looks like: K_max=hν−φ; stopping potential eV₀=K_max

Fast model: Plot/interpret V₀ vs ν with slope h/e.

Intensity and saturation current

Looks like: Photocurrent vs intensity/frequency

Fast model: Intensity → photon rate → saturation current; frequency → K_max.

Bohr hydrogenic levels

Looks like: E_n=−13.6 Z²/n²; transitions

Fast model: Photon energy = |E_i−E_f|; series from final n.

Bohr radius and angular momentum

Looks like: r_n∝n²/Z; L=nħ

Fast model: Use quantized L and Coulomb balance for r,v.

Method 01 · Spectrum split stamp

V changes λ_min; characteristic spikes sit at fixed λ for a target (above threshold).

Do this: Label continuum cut-off vs spikes before answering any X-ray stem.

Method 02 · Moseley straight line

Turns Z-ordering questions into linear readout.

Do this: Plot/think √ν vs Z; intercept relates to screening b.

Method 03 · p before λ

Avoids plugging kinetic energy into photon E=hc/λ by mistake.

Do this: Find momentum first (mv or √(2mK)), then λ=h/p.

Method 04 · Constant choice

Speed without constant hunting; still verify dimensions once.

Do this: Use λ_min≈12400/V Å or λ≈12.27/√V Å for electrons when units match.

Continuous X-ray cutoff

Looks like: λ_min=hc/eV; Duane–Hunt

Fast model: Cutoff fixed by tube voltage, not target Z.

Characteristic X-rays / Moseley

Looks like: Kα, Kβ; √ν = a(Z−b)

Fast model: Vacancies in inner shells; Moseley linear in √f vs Z.

de Broglie matter waves

Looks like: λ=h/p for electrons/protons; accelerating V

Fast model: For electron, p=√(2m eV) nonrelativistically.

Davisson–Germer / Bragg link

Looks like: Constructive interference of matter waves

Fast model: Treat crystal planes as diffraction grating for λ.

Method 01 · Z–A ledger

Decay-chain MCQs become arithmetic, not memory.

Do this: Track Z and A column-wise through each emitted particle.

Method 02 · Exponential in half-lives

Avoids messy e^{−λt} arithmetic under time pressure.

Do this: Prefer N=N₀ / 2^{t/T} when t is a multiple of T_{1/2}.

Method 03 · Mass-defect Q

Consistent atomic masses cancel electron masses in many β decays when done carefully.

Do this: Q = (mass initial − mass final) × 931 MeV/u with the mass type the table uses.

Method 04 · BE/A story

Explains energy release without memorising every reaction.

Do this: Fission: heavy A toward mid-A; fusion: light nuclei toward mid-A — both raise average BE/A.

Radioactive decay law

Looks like: N=N₀ e^{−λt}; T½=ln2/λ

Fast model: Activity A=λN; mean life τ=1/λ.

Binding energy and mass defect

Looks like: Δm c²; BE per nucleon

Fast model: BE = (Zm_H + (A−Z)m_n − M)c² carefully with units.

Fission / fusion Q-value

Looks like: Reaction energy from mass excess

Fast model: Q=(Σm_i−Σm_f)c²; positive Q ⇒ exoergic.

α, β, γ and conservation

Looks like: Identify emission from ΔA, ΔZ

Fast model: α: ΔA=−4, ΔZ=−2; β⁻: Z→Z+1; γ: levels, no ΔZ/ΔA.