Physical Science Formula Sheet
Chapter-wise formula reference for TS SSC Class 10 Physical Science — every key Physics equation and Chemistry formula with variable explanations. Bookmark this before your board exam.
Physics Formulas
Ch. 1, 4, 5, 9, 10Ch. 1 — Reflection of Light at Curved Surfaces
Mirror Formula
1/f = 1/v + 1/u
f = focal length, v = image distance, u = object distance. All measured from pole. New Cartesian sign convention: distances opposite to incident light are negative.
Magnification (Mirror)
m = −v/u = h′/h
h′ = image height, h = object height. m < 0 → inverted (real) image; m > 0 → erect (virtual) image. |m| > 1 → enlarged.
Focal Length and Radius
f = R/2
R = radius of curvature of the mirror. Concave mirror: f is negative; Convex mirror: f is positive (New Cartesian).
Ch. 4 — Refraction of Light at Curved Surfaces
Snell's Law
n₁ sin θ₁ = n₂ sin θ₂
n₁, n₂ = refractive indices of medium 1 and 2; θ₁ = angle of incidence; θ₂ = angle of refraction.
Refractive Index
n = sin i / sin r = c / v
c = speed of light in vacuum (3 × 10⁸ m/s); v = speed of light in the medium. n > 1 for all transparent media.
Lens Formula
1/f = 1/v − 1/u
f = focal length, v = image distance, u = object distance. Distances measured from optical centre.
Magnification (Lens)
m = v/u = h′/h
m > 0 → erect (virtual) image; m < 0 → inverted (real) image.
Power of a Lens
P = 1/f (f in metres)
Power in dioptres (D). Convex (converging) lens: P > 0; Concave (diverging) lens: P < 0.
Combined Power
P = P₁ + P₂
Two thin lenses in contact. Combined focal length: 1/f = 1/f₁ + 1/f₂.
Ch. 5 — Human Eye and Colourful World (Activity)
Near Point / Far Point
Normal eye: near point = 25 cm, far point = ∞
Myopia (nearsightedness): far point < ∞ — corrected with concave lens. Hypermetropia (farsightedness): near point > 25 cm — corrected with convex lens.
Power of Corrective Lens
P = 1/f (f in metres)
For myopia: P = negative (concave). For hypermetropia: P = positive (convex). Presbyopia: bifocal lenses.
Ch. 9 — Electric Current
Ohm's Law
V = IR
V = potential difference (V); I = current (A); R = resistance (Ω). Valid only when temperature is constant.
Resistance of a Conductor
R = ρl/A
ρ = resistivity (Ω·m); l = length (m); A = cross-sectional area (m²). R ∝ l and R ∝ 1/A.
Resistors in Series
R_s = R₁ + R₂ + R₃
Same current through all resistors. Total resistance is the sum. Voltage divides in proportion to resistance.
Resistors in Parallel
1/R_p = 1/R₁ + 1/R₂ + 1/R₃
Same voltage across all. Total resistance is less than the smallest individual resistance. Current divides inversely.
Electric Power
P = VI = I²R = V²/R
P = power (W); V = voltage (V); I = current (A); R = resistance (Ω).
Joule's Law of Heating
H = I²Rt = VIt = Pt
H = heat produced (J); t = time (s). Commercial unit of electrical energy: 1 kWh = 3.6 × 10⁶ J.
Ch. 10 — Electromagnetism (Activity)
Fleming's Left-Hand Rule (Motor)
Thumb → Force (motion); Forefinger → B field; Middle finger → Current
Used to find direction of force on a current-carrying conductor in a magnetic field.
Fleming's Right-Hand Rule (Generator)
Thumb → Motion; Forefinger → B field; Middle finger → Induced current
Used to find direction of induced current in electromagnetic induction.
Chemistry Formulas
Ch. 2, 3, 6, 7, 8, 11, 12Ch. 2 — Chemical Equations and Reactions
Combination Reaction
A + B → AB
Two or more reactants combine to form a single product. Example: CaO + H₂O → Ca(OH)₂
Decomposition Reaction
AB → A + B
A compound breaks into simpler substances. Thermal: 2Pb(NO₃)₂ → 2PbO + 4NO₂ + O₂. Electrolytic: 2H₂O → 2H₂ + O₂.
Single Displacement
A + BC → AC + B
More reactive element displaces less reactive. Example: Fe + CuSO₄ → FeSO₄ + Cu (Fe is more reactive than Cu).
Double Displacement
AB + CD → AD + CB
Exchange of ions between two compounds. Example: Na₂SO₄ + BaCl₂ → BaSO₄↓ + 2NaCl.
Oxidation and Reduction
Oxidation: loss of electrons (or gain of O / loss of H); Reduction: gain of electrons (or loss of O / gain of H)
In a redox reaction, oxidation and reduction occur simultaneously. Reducing agent gets oxidised; oxidising agent gets reduced.
Ch. 3 — Acids, Bases and Salts
Neutralisation
Acid + Base → Salt + Water
Example: HCl + NaOH → NaCl + H₂O. Strength of acid/base depends on degree of ionisation.
pH Scale
pH < 7 → Acidic; pH = 7 → Neutral; pH > 7 → Basic
pH = −log[H⁺]. Strong acids: HCl, H₂SO₄, HNO₃. Strong bases: NaOH, KOH, Ca(OH)₂.
Acid + Metal
Acid + Metal → Salt + Hydrogen gas
Example: Zn + H₂SO₄ → ZnSO₄ + H₂↑. HNO₃ does not give H₂ with metals.
Acid + Metal Carbonate
Acid + Metal Carbonate → Salt + CO₂ + H₂O
Example: Na₂CO₃ + 2HCl → 2NaCl + H₂O + CO₂↑.
Ch. 6 — Structure of Atom
Maximum Electrons per Shell
2n²
n = shell number. K (n=1): 2e⁻; L (n=2): 8e⁻; M (n=3): 18e⁻; N (n=4): 32e⁻.
Valency
Valency = outermost electrons (if ≤ 4), or 8 − outermost electrons (if > 4)
Noble gases: valency = 0. Elements with 1, 2, 3 outer electrons show valency 1, 2, 3 respectively.
Atomic Number and Mass Number
Z = number of protons; A = protons + neutrons; Neutrons = A − Z
Isotopes: same Z, different A. Isobars: same A, different Z. Isotopes of hydrogen: H (1), D (2), T (3).
Ch. 7 — Classification of Elements — The Periodic Table
Modern Periodic Law
Properties of elements are a periodic function of their atomic numbers
Period = row (1–7); Group = column (1–18). Metals on left, non-metals on right, metalloids along the staircase.
Periodic Trends
Atomic size: decreases → across a period (left to right); increases ↓ down a group
Electronegativity: increases → across period. Metallic character: decreases → across period, increases ↓ down group. Valency: increases then decreases across period.
Ch. 8 — Chemical Bonding (Activity)
Ionic Bond
Metal + Non-metal → transfer of electrons → ionic compound
Na→Na⁺ (loses 1e⁻); Cl→Cl⁻ (gains 1e⁻); Na⁺ + Cl⁻ → NaCl. Ionic compounds: high mp, conduct electricity in solution.
Covalent Bond
Non-metal + Non-metal → sharing of electrons
Single bond: 1 shared pair. Double bond: 2 shared pairs. Triple bond: 3 shared pairs. Example: N₂ has triple bond (N≡N).
Ch. 11 — Principles of Metallurgy
Reduction of Metal Oxide
Metal oxide + Carbon → Metal + CO₂
Example: ZnO + C → Zn + CO₂ (carbon reduction). Used for metals of medium reactivity (Fe, Zn, Cu).
Thermite Reaction
Fe₂O₃ + 2Al → Al₂O₃ + 2Fe
Al displaces Fe because Al is more reactive. Highly exothermic — used in welding railway tracks.
Electrolytic Refining
Anode (impure metal) → dissolves; Cathode (pure metal) ← deposits
Used for refining Cu, Ag, Au. Electrolyte = salt solution of the same metal.
Ch. 12 — Carbon and Its Compounds (Activity)
Homologous Series
Each successive member differs by −CH₂− (14 mass units)
Alkanes: CₙH₂ₙ₊₂. Alkenes: CₙH₂ₙ. Alkynes: CₙH₂ₙ₋₂.
Combustion of Hydrocarbons
Hydrocarbon + O₂ → CO₂ + H₂O (+ energy)
Complete combustion → blue flame. Incomplete → yellow sooty flame + CO. Example: CH₄ + 2O₂ → CO₂ + 2H₂O.
Saponification
Ester + NaOH → Soap (sodium salt of fatty acid) + Glycerol
Fat/oil + NaOH (hot) → soap. Soap forms micelles — hydrophilic head (water-loving) + hydrophobic tail (water-fearing).