Class 10 Physics Formulas

Cheatsheet Content

### Light: Reflection - **Law of Reflection:** - Angle of incidence = Angle of reflection ($\angle i = \angle r$) - Incident ray, reflected ray, and normal all lie in the same plane. - **Mirror Formula:** $$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$$ - $f$: focal length - $v$: image distance - $u$: object distance - **Magnification (m):** $$m = \frac{h'}{h} = -\frac{v}{u}$$ - $h'$: height of image - $h$: height of object - **Sign Convention (Cartesian):** - Pole is origin (0,0). - Object always placed to the left. - Distances to the right of pole are positive. - Distances to the left of pole are negative. - Heights above principal axis are positive. - Heights below principal axis are negative. - **Concave Mirror:** Focal length (f) is negative. - **Convex Mirror:** Focal length (f) is positive. ### Light: Refraction - **Snell's Law:** $$n_1 \sin i = n_2 \sin r$$ - $n_1$: refractive index of medium 1 - $n_2$: refractive index of medium 2 - $i$: angle of incidence - $r$: angle of refraction - **Refractive Index (n):** $$n = \frac{\text{speed of light in vacuum (c)}}{\text{speed of light in medium (v)}} = \frac{c}{v}$$ - **Lens Formula:** $$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$ - $f$: focal length - $v$: image distance - $u$: object distance - **Magnification (m):** $$m = \frac{h'}{h} = \frac{v}{u}$$ - **Power of a Lens (P):** $$P = \frac{1}{f \text{ (in metres)}}$$ - Unit: Dioptre (D) - Convex lens: Positive power - Concave lens: Negative power - **Combination of Lenses:** $$P_{net} = P_1 + P_2 + ...$$ $$f_{net} = \frac{1}{P_{net}}$$ - **Convex Lens:** Focal length (f) is positive. - **Concave Lens:** Focal length (f) is negative. ### Human Eye & Colourful World - **Least Distance of Distinct Vision:** ~25 cm (for a normal eye) - **Power of Accommodation:** Ability of the eye lens to adjust its focal length. - **Myopia (Nearsightedness):** Corrected by a concave lens. - **Hypermetropia (Farsightedness):** Corrected by a convex lens. - **Presbyopia:** Corrected by bifocal lenses. - **Scattering of Light:** Responsible for blue sky, red sunset/sunrise. ### Electricity - **Electric Current (I):** $$I = \frac{Q}{t}$$ - $Q$: charge (Coulombs, C) - $t$: time (seconds, s) - Unit: Ampere (A) - **Ohm's Law:** $$V = IR$$ - $V$: potential difference (Volts, V) - $I$: current (Amperes, A) - $R$: resistance (Ohms, $\Omega$) - **Resistance (R):** $$R = \rho \frac{L}{A}$$ - $\rho$: resistivity ($\Omega \cdot m$) - $L$: length of conductor (m) - $A$: area of cross-section ($m^2$) - **Resistors in Series:** $$R_{eq} = R_1 + R_2 + R_3 + ...$$ - **Resistors in Parallel:** $$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ...$$ - **Electric Power (P):** $$P = VI$$ $$P = I^2R$$ $$P = \frac{V^2}{R}$$ - Unit: Watt (W) - **Electrical Energy (E):** $$E = P \times t$$ $$E = VIt$$ $$E = I^2Rt$$ $$E = \frac{V^2}{R}t$$ - Unit: Joule (J) - Commercial unit: kilowatt-hour (kWh) - 1 kWh = $3.6 \times 10^6$ J - **Heat Produced (Joule's Law of Heating, H):** $$H = I^2Rt$$ - **Potential Difference (V):** $$V = \frac{W}{Q}$$ - $W$: work done (Joules, J) - $Q$: charge (Coulombs, C) ### Magnetic Effects of Electric Current - **Fleming's Left-Hand Rule (for motor):** - Thumb: Direction of Force (Motion) - Forefinger: Direction of Magnetic Field - Middle Finger: Direction of Current - **Fleming's Right-Hand Rule (for generator):** - Thumb: Direction of Motion - Forefinger: Direction of Magnetic Field - Middle Finger: Direction of Induced Current - **Magnetic Field Lines:** - Emerge from North pole, merge into South pole outside magnet. - Inside magnet, from South to North. - Never intersect. - Stronger where lines are closer. ### Sources of Energy - **Renewable Sources:** Solar, Wind, Hydro, Biomass, Geothermal. - **Non-Renewable Sources:** Fossil Fuels (Coal, Petroleum, Natural Gas), Nuclear Fuels. - **Solar Energy Devices:** Solar cooker, solar water heater, solar cells. - **Wind Energy:** Requires wind speed > 15 km/h. - **Hydro Energy:** From flowing water. - **Biomass:** From organic matter. - **Nuclear Energy:** From nuclear fission (e.g., Uranium).