Mirror formula

“Holding a makeup concave mirror a few centimeters from your face shows a virtual image that looks larger than your actual face.”

For spherical mirrors the mirror formula 1/v + 1/u = 1/f holds with the sign convention: distances measured opposite to incident light are negative. Concave mirrors have f < 0, convex f > 0. A common trap is using a positive f for a concave mirror, which gives an impossible image position.

1/v + 1/u = 1/f

Memory trick: Concave f = negative (C = Cold), Convex f = positive.

Semiconductors: n-type vs p-type

“n-type silicon is like a subway car packed with extra passengers (electrons); p-type is a car with many empty seats (holes).”

In n-type, donor atoms add free electrons; in p-type, acceptor atoms create holes. Conductivity comes from majority carriers. Trap: ‘n’ means electrons (negative), not neutron, and ‘p’ means holes (positive).

Memory trick: n = extra e⁻, p = missing e⁻ (holes)

Speed and field ratio — common mistake

“Gamma rays from a hospital PET scanner and FM radio broadcasts arrive at the same satellite together, both moving at the universal light speed.”

All electromagnetic waves—radio, microwave, infrared, visible, ultraviolet, X-ray, gamma—propagate in vacuum at exactly c. Their field ratio E₀⁄B₀ equals c, and only photon energy (E = hν) varies with frequency. Mistaking γ-rays as faster is a common error.

Memory trick: All EM waves share the same c, any ν

Relative velocity in two dimensions — common mistake

“A swimmer aims straight across a river but ends up downstream; the downstream drift shows the river’s velocity added vectorially.”

For relative motion, always subtract the observer’s velocity vector: v_A/B = v_A – v_B. Adding speeds as numbers ignores direction and gives a wrong resultant. The common mistake is treating v_A and v_B as scalars.

Memory trick: Never add speeds, add vectors: v_rel = v – v_obs

Conduction, convection and radiation

“A hot iron skillet heats a pot on the stove mainly by conduction through the metal contact.”

Conduction transfers energy by microscopic collisions in solids, convection carries heat with bulk fluid motion, and radiation moves energy as electromagnetic waves, needing no material medium. Real situations often involve more than one mode. The exam trap: assuming solar heat reaches Earth by convection—only radiation works across vacuum.

Memory trick: Conduction = Contact, Convection = Current, Radiation = Rays.

Degrees of freedom — common mistake

“Treating every gas like air is like using one size for all shoes – it ignores the molecule’s shape.”

The common error is to assign the same DoF count to every gas regardless of temperature. Translational DoF are always 3, but rotational and vibrational DoF depend on molecular geometry and whether the temperature can excite vibrations. Ignoring these variations gives wrong C_V and γ.

Memory trick: Check shape & temperature before fixing DoF

Capacitance and geometry — common mistake

“A coffee mug’s size decides how much coffee it holds, not how full you pour it.”

Capacitance C = Q/V is set by plate area, separation and dielectric (C = εA/d); it does not depend on the amount of charge or the voltage applied. If Q changes, V changes proportionally, but C stays the same unless geometry or ε changes. The exam trap is to claim “more charge raises C” – only geometry matters.

Memory trick: C = ε·A/d → bigger A, smaller d → larger C

Dia-, para- and ferromagnetism — common mistake

“A compass needle snaps to a steel nail (strong pull) but barely shifts near a glass of water (tiny push).”

Diamagnets have χ < 0 and show a very weak repulsion; paramagnets have χ > 0 but tiny, giving a weak attraction; ferromagnets have χ ≫ 1, strong attraction, domain alignment and retain magnetisation. The exam trap is to label any attracted substance as ferromagnetic – check the magnitude and sign of χ, not just the direction of force.

Memory trick: Dia = Distant (repel), Para = Partial (weak attract), Ferro = Forceful (strong domains)

Spectral series — common mistake

“When a spectroscope shows a line from n=4 → n=2, it belongs to the Balmer series, not a new “n=4” series.”

The series name is fixed by the final level, not the starting one. All lines that end at n=2 form the Balmer series, regardless of the upper n. A common error is calling the transition “n=4 series”; the correct label is Balmer.

Memory trick: Name = where it lands.

Activity

“The tiny 241Am source in a smoke detector loses its ionising power exactly as A = λN, so the detector’s current drops exponentially over years.”

Activity A is the number of decays per second, given by A = λN where λ is the decay constant and N the number of undecayed nuclei. Measured count rate (cps) must be corrected for detector efficiency, geometry and dead-time; otherwise cps is mistaken for true activity.

Memory trick: A = λN → Activity = λ × N (A for Activity, λ for loss rate)

Significant figures in results — common mistake

“If you cut a 12.345 cm wire into pieces and round each piece to 12 cm before adding, the total length is off.”

Rounding each intermediate value reduces the final precision. Keep extra (guard) digits through all operations and round only the final answer to the correct number of significant figures. The common exam error is to round after each step, which gives a less accurate result.

Memory trick: Carry guard digits, round final answer only.

Doppler effect — common mistake

“When an ambulance rushes past, its siren pitch rises as it approaches and drops as it recedes.”

The observed frequency f' changes because the rate at which wavefronts reach the observer is altered by relative motion. Use f' = (v ± v_o)/(v ∓ v_s)·f_s, adding v_o when the observer moves toward the source and subtracting v_s when the source moves toward the observer. A common trap is to flip the sign in the denominator; the source speed always carries the opposite sign to its motion relative to the observer.

Memory trick: Approach → higher pitch: +v_o, –v_s; Recede → lower pitch: –v_o, +v_s.

Ampere's circuital law — common mistake

“Trying to find B around a bent wire is like expecting the same wind speed on a curved road – it changes with the curve.”

Ampere’s law gives the total enclosed current, not the local field distribution. Assuming B is uniform for any wire shape ignores that B’s direction and magnitude depend on geometry; only symmetric cases let you replace B by a constant in the integral. The exam trap is equating ∮B·dl = B·(perimeter) without checking symmetry.

Memory trick: Only symmetric loops → B constant

interference vs diffraction

“A laser through two slits makes equally spaced dots (interference); through one slit it paints a wide central bar (diffraction).”

Interference arises from two or more coherent sources, producing equally spaced bright and dark fringes of uniform width. Diffraction is the spreading of a wave from a single aperture, giving a broad central maximum whose width ≈2λD/a and subsidiary minima. A common trap is treating diffraction fringes as equally spaced like interference.

Memory trick: Interf = many → equal dots; Diff = one → broad bar

resistance vs reactance

“A toaster’s heating element uses resistance, while the motor of a ceiling fan relies on the capacitor’s reactance to start.”

Resistance dissipates energy as heat and is independent of frequency (R constant). Inductive reactance X_L = ωL increases linearly with f, whereas capacitive reactance X_C = 1/(ωC) decreases as 1/f. Only reactance varies with frequency; a frequent trap is treating X_L and X_C the same way or adding R and X directly.

Memory trick: R steady, L ↑ with f, C ↓ with f

Dimensional analysis — common mistake

“Using the period formula T=2π√(L/g) you see L/g has dimensions of time², but forgetting the π shows the equation is still dimensionally right yet numerically off.”

A common pitfall is assuming that dimensional consistency guarantees correctness. Dimensionless numbers such as 2, π, or √2 do not appear in dimensional checks, so a missing factor can slip through. In JEE, after a dimensional check, compare the full numerical coefficient to catch such errors.

Memory trick: Dim-check ≠ numeric check; watch for hidden constants.

Relative velocity

“Walking forward on a train moving east makes your ground speed the sum of your walk speed and the train’s speed.”

Relative velocity of A w.r.t B is vAB = vA – vB, a vector subtraction. If both move same direction, subtract magnitudes; opposite directions the subtraction flips sign, effectively adding speeds. Keep direction in mind.

v(AB) = v(A) − v(B)

Memory trick: vAB = vA – vB; opposite → add

Banking of roads

“When a car rounds a banked curve, the road’s tilt pushes the car inward, letting it turn without skidding.”

For a banked road of angle θ, the component of the normal force provides the required centripetal force, giving tanθ = v²/(rg). If friction is neglected, this relation holds exactly. Exam trap: using tanθ = μs + v²/rg incorrectly; the formula is only for frictionless banking.

tanθ = v²/rg

Memory trick: Bank angle → tanθ = v²/rg (no friction).

Coefficient of restitution

“A rubber ball hitting the floor bounces high, showing a restitution coefficient close to 1.”

The coefficient of restitution e = (relative speed after collision)/(relative speed before collision) measures bounciness; e = 1 for perfectly elastic, e = 0 for perfectly inelastic. It is dimensionless and lies between 0 and 1. Trap: swapping numerator and denominator gives >1.

Memory trick: e = speed-after ÷ speed-before, 0≤e≤1

Angular momentum

“When a figure skater pulls her arms in, her spin rate jumps while total angular momentum stays the same.”

Angular momentum L equals I ω. In the absence of external torque, L is conserved, so any change in I must be compensated by an opposite change in ω. Students often assume ω stays constant when the mass distribution changes, leading to wrong answers.

Memory trick: L constant → if I ↓, ω ↑

Acceleration due to gravity g

“A miner’s scale reads a few grams lighter 2 km below ground because the Earth’s pull weakens with depth.”

At the surface g = GM/R². Inside a uniform Earth the field is g(r)=GM_enc/r² = g₀·(r/R). Thus for a small height h above the surface g≈g₀(1-2h/R) and for a small depth d below it g≈g₀(1-d/R). By the shell theorem only the mass inside radius r contributes; mass outside gives zero net force. A frequent trap is using the altitude-only (-2h/R) factor for depth, which gives a wrong answer.

Memory trick: Depth d → r=R-d → g≈g₀(1-d/R); only interior mass matters.

Viscosity — common mistake

“Honey clings to a spoon while water rushes off, a clear sign of higher internal friction.”

Viscosity measures a fluid’s internal friction; it resists relative motion between adjacent layers. Higher viscosity (e.g., honey) means slower flow under the same driving force, while low viscosity (e.g., water) flows readily. Students often assume all liquids have the same viscosity or ignore temperature effects.

Memory trick: Viscous = thick → flow slow.

Elastic energy

“Stretching a spring slowly stores energy, just like pulling back a bow stores the arrow’s launch energy.”

Work done in stretching an elastic body in the linear (Hooke’s law) region is stored as elastic potential energy. Energy density = ½ σ ε (stress × strain) = area of triangle under the stress-strain curve. Remember the ½ factor comes from the force increasing from zero to its final value.

Memory trick: Energy = ½ (σ × ε) – triangle area

Stationary waves

“Plucking a guitar string makes fixed nodes at the ends while the middle vibrates.”

Two identical waves traveling opposite directions superpose to give standing waves with stationary nodes (zero displacement) and antinodes (maximum displacement). A common mistake is assuming nodes move.

Memory trick: Nodes = zero, Antinodes = max swing