Every formula, rule and key fact in the latest NCERT Class 10 Science book.
Light — reflection and refraction#
| Quantity |
Formula |
| Radius of curvature |
$R = 2f$ |
| Mirror formula |
$\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$ |
| Magnification (mirror) |
$m = \dfrac{h'}{h} = -\dfrac{v}{u}$ |
| Lens formula |
$\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$ |
| Magnification (lens) |
$m = \dfrac{h'}{h} = \dfrac{v}{u}$ |
| Snell’s law |
$\dfrac{\sin i}{\sin r} = \text{constant}$ |
| Absolute refractive index |
$n_m = \dfrac{c}{v}$ |
| Relative refractive index |
$n_{21} = \dfrac{v_1}{v_2}$ |
| Power of a lens |
$P = \dfrac{1}{f}$ |
| Lenses in contact |
$P = P_1 + P_2 + P_3 + \cdots$ |
| Formula |
Explanation and notes |
| Radius of curvature |
$R$ = radius of curvature, $f$ = focal length. Holds for spherical mirrors of small aperture. |
| Mirror formula |
$u$ = object distance, $v$ = image distance, $f$ = focal length, all measured from the pole. Has a + sign. |
| Magnification (mirror) |
$h$ = object height, $h'$ = image height. Has a minus sign. |
| Lens formula |
Distances measured from the optical centre. Has a − sign. |
| Magnification (lens) |
No minus sign. |
| Snell’s law |
$i$ = angle of incidence, $r$ = angle of refraction. The constant is the refractive index of medium 2 with respect to medium 1, for a given pair of media and colour of light. |
| Absolute refractive index |
$c$ = speed of light in vacuum ($3 \times 10^8$ m/s), $v$ = speed of light in the medium. No unit. |
| Relative refractive index |
$v_1$, $v_2$ = speed of light in medium 1 and medium 2. Higher $n$ means optically denser. |
| Power of a lens |
$f$ must be in metres. Unit: dioptre (D); 1 D is the power of a lens with $f$ = 1 m. |
| Lenses in contact |
Net power is the sum of the individual powers, with signs. |
Laws#
| Law |
Statement |
| Reflection 1 |
$\angle i = \angle r$ |
| Reflection 2 |
Incident ray, normal and reflected ray lie in the same plane |
| Refraction 1 |
Incident ray, refracted ray and normal lie in the same plane |
| Refraction 2 (Snell’s law) |
$\dfrac{\sin i}{\sin r}$ is constant for a given pair of media and colour of light |
| Rarer → denser |
Light bends towards the normal |
| Denser → rarer |
Light bends away from the normal |
New Cartesian sign convention#
| Quantity |
Sign |
| Object position |
Always on the left, so $u$ is always negative |
| Distances measured from |
Pole (mirror) or optical centre (lens) |
| Along incident light (right) |
Positive |
| Against incident light (left) |
Negative |
| Height above the principal axis |
Positive |
| Height below the principal axis |
Negative |
Mirror and lens signs#
|
Concave mirror |
Convex mirror |
Convex lens |
Concave lens |
| Type |
Converging |
Diverging |
Converging |
Diverging |
| Focal length $f$ |
Negative |
Positive |
Positive |
Negative |
| Power $P$ |
— |
— |
Positive |
Negative |
| Real image possible? |
Yes |
No |
Yes |
No |
| Magnification |
Meaning |
| $m$ negative |
Real, inverted image |
| $m$ positive |
Virtual, erect image |
| $\lvert m \rvert > 1$ |
Enlarged |
| $\lvert m \rvert < 1$ |
Diminished |
Positions in brackets are for the lens (F₁, 2F₁ and O in place of F, C and P).
| Object at |
Concave mirror image |
Convex lens image |
Size and nature |
| Infinity |
F |
F₂ |
Highly diminished, real, inverted |
| Beyond C (2F₁) |
Between F and C |
Between F₂ and 2F₂ |
Diminished, real, inverted |
| At C (2F₁) |
C |
2F₂ |
Same size, real, inverted |
| Between C and F (2F₁ and F₁) |
Beyond C |
Beyond 2F₂ |
Enlarged, real, inverted |
| At F (F₁) |
Infinity |
Infinity |
Highly enlarged, real, inverted |
| Between P and F (F₁ and O) |
Behind the mirror |
Same side as the object |
Enlarged, virtual, erect |
| Object at |
Convex mirror image |
Concave lens image |
Size and nature |
| Infinity |
F, behind |
F₁ |
Highly diminished, virtual, erect |
| Between infinity and P (O) |
Between P and F, behind |
Between F₁ and O |
Diminished, virtual, erect |
Plane mirror, uses and key values#
| Item |
Detail |
| Plane mirror image |
Virtual, erect, same size, as far behind as the object is in front, laterally inverted |
| Concave mirror uses |
Torches, searchlights, headlights, shaving mirrors, dentists’ mirrors, solar furnaces |
| Convex mirror uses |
Rear-view mirrors (always erect image, wider field of view) |
| Refractive index |
Water 1.33, kerosene 1.44, crown glass 1.52, diamond 2.42 |
Human eye and colourful world#
- Near point of a normal eye: 25 cm. Far point: infinity.
- Myopia → concave lens. Hypermetropia → convex lens. Presbyopia → bifocal lens.
- Spectrum: VIBGYOR. Violet bends most, red least.
- Blue sky: scattering by air molecules. Red sunset: long path through air. Danger signals red: least scattered.
- Stars twinkle (atmospheric refraction); planets do not. Sunrise seen about 2 minutes early.
Electricity#
| Quantity |
Formula |
| Electric current |
$I = \dfrac{Q}{t}$ |
| Potential difference |
$V = \dfrac{W}{Q}$ |
| Ohm’s law |
$V = IR$ |
| Resistance of a wire |
$R = \rho\dfrac{l}{A}$ |
| Resistors in series |
$R_s = R_1 + R_2 + R_3$ |
| Resistors in parallel |
$\dfrac{1}{R_p} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3}$ |
| Heating effect (Joule’s law) |
$H = I^2Rt$ |
| Electric power |
$P = VI = I^2R = \dfrac{V^2}{R}$ |
| Formula |
Explanation and notes |
| Electric current |
$Q$ = charge (coulomb, C), $t$ = time (s). Unit: ampere (A) = C/s. |
| Potential difference |
$W$ = work done (J), $Q$ = charge (C). Unit: volt (V) = J/C. |
| Ohm’s law |
Holds when temperature stays the same. Unit of $R$: ohm (Ω) = V/A. |
| Resistance of a wire |
$\rho$ = resistivity (Ω m), $l$ = length, $A$ = area of cross-section. $R$ doubles if length doubles; falls if area increases. |
| Resistors in series |
Same current through each. Total is more than the largest resistance. |
| Resistors in parallel |
Same potential difference across each. Total is less than the smallest resistance. |
| Heating effect |
$H$ in joules. Heat depends on current squared, resistance and time. |
| Electric power |
Unit: watt (W) = J/s. Commercial unit of energy: $1 \text{ kWh} = 3.6 \times 10^6 \text{ J}$. |
Key values#
| Fact |
Value |
| Charge on an electron |
$1.6 \times 10^{-19}$ C |
| Electrons in 1 C |
About $6 \times 10^{18}$ |
| Ammeter |
Connected in series |
| Voltmeter |
Connected in parallel |
Magnetic effects of current#
- Field lines: N → S outside, S → N inside; closed curves; never cross.
- Right-hand thumb rule: thumb = current, curled fingers = field.
- Fleming’s left-hand rule: forefinger = field, middle finger = current, thumb = force.
- Household supply: 220 V, 50 Hz AC. Live = red, neutral = black, earth = green.
Chemistry — key reactions#
| Reaction |
Equation |
| Quick lime + water |
$\text{CaO} + \text{H}_2\text{O} \rightarrow \text{Ca(OH)}_2$ |
| Electrolysis of water |
$2\text{H}_2\text{O} \rightarrow 2\text{H}_2 + \text{O}_2$ (H₂ : O₂ = 2 : 1 by volume) |
| Displacement |
$\text{Fe} + \text{CuSO}_4 \rightarrow \text{FeSO}_4 + \text{Cu}$ |
| Precipitation |
$\text{Na}_2\text{SO}_4 + \text{BaCl}_2 \rightarrow \text{BaSO}_4 + 2\text{NaCl}$ |
| Neutralisation |
Acid + base → salt + water |
| Acid + carbonate |
Salt + water + CO₂ (turns lime water milky) |
| Chlor-alkali process |
$2\text{NaCl} + 2\text{H}_2\text{O} \rightarrow 2\text{NaOH} + \text{Cl}_2 + \text{H}_2$ |
| Baking soda on heating |
$2\text{NaHCO}_3 \rightarrow \text{Na}_2\text{CO}_3 + \text{H}_2\text{O} + \text{CO}_2$ |
| Thermit reaction |
$\text{Fe}_2\text{O}_3 + 2\text{Al} \rightarrow 2\text{Fe} + \text{Al}_2\text{O}_3$ + heat |
| Esterification |
Ethanoic acid + ethanol → ester + water |
- pH: below 7 acidic, 7 neutral, above 7 basic. Tooth decay below pH 5.5.
- Reactivity series: K > Na > Ca > Mg > Al > Zn > Fe > Pb > [H] > Cu > Hg > Ag > Au
- Plaster of Paris: CaSO₄·½H₂O. Gypsum: CaSO₄·2H₂O. Washing soda: Na₂CO₃·10H₂O. Bleaching powder: CaOCl₂.
Carbon compounds#
| Series |
General formula |
First member |
| Alkane |
$\text{C}_n\text{H}_{2n+2}$ |
Methane CH₄ |
| Alkene |
$\text{C}_n\text{H}_{2n}$ |
Ethene C₂H₄ |
| Alkyne |
$\text{C}_n\text{H}_{2n-2}$ |
Ethyne C₂H₂ |
- Successive members differ by –CH₂– (14 u).
- Suffixes: alcohol -ol, aldehyde -al, ketone -one, carboxylic acid -oic acid.
Biology — key facts#
- Photosynthesis: $6\text{CO}_2 + 12\text{H}_2\text{O} \rightarrow \text{C}_6\text{H}_{12}\text{O}_6 + 6\text{O}_2 + 6\text{H}_2\text{O}$ (sunlight, chlorophyll)
- Aerobic respiration (mitochondria) → CO₂ + water. Yeast (anaerobic) → ethanol + CO₂. Muscles (low oxygen) → lactic acid.
- Human heart: 4 chambers; double circulation. Normal blood pressure: about 120/80 mm Hg.
- Monohybrid F2 ratio 3 : 1 (genotype 1 : 2 : 1). Dihybrid F2 ratio 9 : 3 : 3 : 1.
- Sex chromosomes: female XX, male XY. The father’s sperm decides the sex.
Environment#
- Plants capture about 1% of sunlight. 10% law: 10% of energy passes to the next trophic level.
- Ozone formation: $\text{O}_2 \rightarrow \text{O} + \text{O}$, then $\text{O} + \text{O}_2 \rightarrow \text{O}_3$ (UV). Depleted by CFCs; UNEP agreement in 1987.