Physics — Complete Formula Sheet

Angle of incidence equals angle of reflection; both measured from the normal. Incident ray, reflected ray and normal lie in the same plane.

$u$: Object distance from pole (m); negative for real object · $v$: Image distance from pole (m) · $f$: Focal length (m); negative for concave, positive for convex mirror

Relates object distance u, image distance v and focal length f of a spherical mirror. Uses sign convention.

Ratio of image height to object height. Negative m ⇒ real, inverted image.

Focal length equals half the radius of curvature (for both spherical mirrors and thin spherical surfaces).

$n$: Refractive index (dimensionless) · $i,r$: Angles of incidence and refraction · $v_1,v_2$: Speed of light in the two media (m/s)

Snell's law: ratio of sines equals ratio of speeds. n = c/v (absolute).

c = speed of light in vacuum (3 × 10⁸ m/s); v = speed in the medium. Always ≥ 1 for real materials.

Note the MINUS sign (differs from mirror formula). u negative for real object; f positive for convex, negative for concave lens.

For lens, m = v/u (no minus sign). Positive m ⇒ virtual erect image.

Unit: dioptre (D). Positive for converging (convex), negative for diverging (concave) lens.

Powers add algebraically (with sign). Very common in board numericals.

Ability of the eye lens to change focal length via ciliary muscles. Range: about 2 D for a normal adult eye.

For a normal adult eye, the near point is 25 cm from the eye. Far point = infinity.

Use a concave lens whose focal length equals the (negative of) far point. Then image of infinity forms at the far point.

y = defective near point (>25 cm), D = 25 cm. Formula gives positive f ⇒ convex lens.

Concave lens ⇒ negative P (for myopia). Convex lens ⇒ positive P (for hypermetropia).

A = angle of prism. Minimum deviation occurs when i₁ = i₂ (symmetric passage).

Shorter wavelengths (blue) scatter much more than longer (red). Explains blue sky and red Sun at sunset.

Applied at both refracting surfaces of the prism. Wavelength-dependent n causes dispersion.

$I$: Current (ampere, A) · $Q$: Charge (coulomb, C) · $t$: Time (second, s)

Rate of flow of charge. 1 A = 1 C/s. Ammeter connected in series.

$V$: Potential difference (volt, V) · $W$: Work done (joule, J) · $Q$: Charge moved (C)

Work done per unit charge to move it from one point to another. Voltmeter in parallel.

Current through a metallic conductor is directly proportional to potential difference (constant T).

$R$: Resistance (ohm, Ω) · $\rho$: Resistivity of the material (Ω·m) · $l$: Length of the conductor (m) · $A$: Area of cross-section (m²)

Resistance is proportional to length and inversely proportional to area of cross-section.

Same current through each resistor; voltages add. R_s is always LARGER than the largest resistor.

Same voltage across each; currents add. R_p is always SMALLER than the smallest resistor.

Three forms — pick whichever avoids the unknown quantity. Unit: watt (W).

Commercial unit: 1 kWh = 3.6 × 10⁶ J (also called 1 unit of electricity).

Heat produced in a resistor when current flows through it. Basis of electric heater, iron, bulb filament.

One 'unit' on the electricity bill. Multiply kW by hours to get kWh.

$B$: Magnetic field (tesla, T) · $I$: Current in the wire (A) · $r$: Perpendicular distance from wire (m)

Field forms concentric circles around a long straight wire. Stronger with more current, weaker farther away.

Grip the wire with the right hand, thumb along current — fingers curl in the direction of B.

At the centre of a loop of radius r. For N turns, B becomes N × (that value).

${\mu }_0$: Permeability of free space = 4π × 10⁻⁷ T·m/A · $n$: Number of turns per metre (m⁻¹) · $I$: Current in the solenoid (A)

Uniform field inside a long solenoid. n = turns per unit length. Field pattern is like a bar magnet.

Maximum when B ⊥ I. Direction given by Fleming's LEFT-hand rule.

Stretch thumb, forefinger and middle finger of LEFT hand mutually perpendicular — gives force direction. Basis of the electric MOTOR.

RIGHT hand: thumb (motion), forefinger (field), middle (induced current). Basis of the GENERATOR.

An EMF is induced in a coil whenever the magnetic flux linked with it changes. Faster the change, larger the EMF.

In India: V = 220 V AC, 50 Hz. Fuse rating chosen slightly above the appliance's normal current I = P/V.