PhysicsLight — Reflection and Refraction
Mirror formula
$\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$
Magnification (mirror)
$m = -\dfrac{v}{u} = \dfrac{h'}{h}$
Focal length and radius of curvature
$f = \dfrac{R}{2}$
Lens formula
$\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$
Magnification (lens)
$m = \dfrac{v}{u} = \dfrac{h'}{h}$
Power of a lens
$P = \dfrac{1}{f\ (\text{in metres})}$, unit: dioptre (D)
Refractive index
$n = \dfrac{c}{v} = \dfrac{\sin i}{\sin r}$ (Snell's law)
PhysicsThe Human Eye and the Colourful World
Power of a lens (corrective lenses)
$P = \dfrac{1}{f}$ (f in metres); concave lens for myopia (−), convex lens for hypermetropia (+).
Range of clear vision
Near point $\approx 25\ \text{cm}$; far point $= \infty$ for a normal eye.
Lens formula (for the corrective lens)
$\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$
PhysicsElectricity
Ohm's law
$V = IR$
Charge and current
$Q = It$
Resistance of a conductor
$R = \rho\dfrac{L}{A}$ ($\rho$ = resistivity)
Resistors in series
$R_s = R_1 + R_2 + R_3 + \cdots$
Resistors in parallel
$\dfrac{1}{R_p} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3} + \cdots$
Electric power
$P = VI = I^2 R = \dfrac{V^2}{R}$
Electrical energy
$E = Pt$; 1 unit $= 1\ \text{kWh} = 3.6 \times 10^6\ \text{J}$
ChemistryAcids, Bases and Salts — the pH Scale
pH scale
Runs from $0$ to $14$. $\text{pH} \lt 7$: acidic; $\text{pH} = 7$: neutral; $\text{pH} \gt 7$: basic (alkaline).
Stronger acid / base
The lower the pH, the more acidic the solution; the higher the pH, the more basic.
Neutralisation reaction
$\text{Acid} + \text{Base} \rightarrow \text{Salt} + \text{Water}$
Frequently asked questions
- What is the mirror formula and lens formula?
- Mirror: $\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}$; Lens: $\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}$.
- What is the power of a lens?
- $P = \dfrac{1}{f}$ (f in metres), unit dioptre (D); convex lens positive, concave negative.
- What is the formula for electric power?
- $P = VI = I^2R = \dfrac{V^2}{R}$; energy $E = Pt$ (1 unit = 1 kWh).
- What does the pH scale measure?
- It measures how acidic or basic a solution is, from 0 to 14 (7 is neutral).
These formulas follow the latest CBSE / NCERT Class 10 Science syllabus. (The numerical chapters in Class 10 Science are Light, the Human Eye and Electricity.) For worked examples, open the full NCERT solutions linked above.