Physical Environment

In physical science, a force is an external agent that changes or tends to change the state of rest or uniform motion of a body in a straight line.

• Contact Forces (স্পর্শ বল): Require direct physical interaction between bodies, e.g., muscular force, normal reaction, and frictional force (ঘর্ষণ বল) which always opposes relative motion at contact surfaces.
• Non-Contact Forces / Action-at-a-Distance (স্পর্শহীন বল): Act across empty space without physical touch: Gravitational force, Electrostatic force (between electric charges), and Magnetic force (between magnetic poles).

The rate of change of momentum of a body is directly proportional to the applied unbalanced force and takes place in the direction of the force. Quantitatively:
$$\mathbf{F = m \cdot a}$$

• SI Unit: Newton (N). $1\text{ N}$ is the force that imparts an acceleration of $1\text{ m/s}^2$ to a mass of $1\text{ kg}$.
• CGS Unit: Dyne. $1\text{ dyne} = 1\text{ g} \times 1\text{ cm/s}^2$.
• Conversion Factor: $1\text{ N} = 10^3\text{ g} \times 10^2\text{ cm/s}^2 = \mathbf{10^5\text{ dynes}}$.

It is vital to distinguish between a body's inertia and the gravitational pull acting upon it:

Every particle of matter in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers:

$$\mathbf{F = G \frac{m_1 m_2}{r^2}}$$

• Universal Gravitational Constant ($G$): The attractive force between two unit masses placed at unit distance apart. In SI: $\mathbf{G = 6.673 \times 10^{-11}\text{ N}\cdot\text{m}^2/\text{kg}^2}$; in CGS: $6.673 \times 10^{-8}\text{ dyn}\cdot\text{cm}^2/\text{g}^2$.
• $G$ is called universal because its numerical value is independent of the nature of the intervening medium, temperature, or chemical state of the bodies.

The perpendicular force acting on a unit surface area is defined as pressure (চাপ):

$$\mathbf{P = \frac{\text{Thrust (লম্ব বল)}}{\text{Area (ক্ষেত্রফল)}} = \frac{F}{A}}$$

• SI Unit: Pascal (Pa), where $1\text{ Pa} = 1\text{ N/m}^2$. CGS Unit: $\text{dyne/cm}^2$ ($1\text{ Pa} = 10\text{ dyne/cm}^2$).
• Inverse Area Relation: For a given force, $P \propto \frac{1}{A}$. That is why a sharp nail pierces wood easily with minimal strike force, while a blunt nail requires massive blows; similarly, cutting knives have razor-thin edges, and heavy trucks have double/triple wide tires to reduce ground pressure.

Consider a horizontal liquid layer at depth $h$ in a fluid of uniform density $\rho$. The weight of the vertical liquid column above an area $A$ is $W = m g = (\text{Volume} \times \rho) g = (A \cdot h) \rho g$. Therefore, the hydrostatic pressure is:

$$\mathbf{P = \frac{\text{Weight}}{\text{Area}} = \frac{A \cdot h \rho g}{A} = h \cdot \rho \cdot g}$$

Key Deductions:

• Hydrostatic pressure is independent of the shape, surface area, or total volume of the container (Hydrostatic Paradox).
• Pressure increases linearly with depth ($P \propto h$) and fluid density ($P \propto \rho$).

Liquids in static equilibrium exhibit distinct isotropic properties:

• Equality in All Directions (Pascal's Principle): Liquid pressure at any given interior point acts with equal intensity in all directions (downward, upward, and laterally).
• Horizontal Isobaric Surfaces: At the same vertical depth in a homogeneous liquid, the pressure is identical everywhere.
• Perpendicular Thrust: Liquid pressure always exerts force strictly normal (perpendicular) to the containing walls.
• Principle of Communicating Vessels (তরলের সমোচ্চশীলতা ধর্ম): In interconnected vessels of different shapes and cross-sections, an unconfined liquid settles at the exact same horizontal level across all branches.

When an object is wholly or partially immersed in a fluid, the hydrostatic pressure acting on its bottom surface (at greater depth $h_2$) exceeds the downward pressure on its top surface (at shallower depth $h_1$). This upward resultant force is called Buoyant Force or Upthrust (প্লবতা, $F_b$):

$$F_b = (P_2 - P_1) A = (h_2 - h_1) \rho g A = V_{\text{sub}} \cdot \rho \cdot g$$

where $V_{\text{sub}}$ is the volume of the submerged portion of the object and $\rho$ is the density of the surrounding fluid.

Archimedes' Formal Statement: When a solid body is wholly or partially immersed in a liquid (or gas) at rest, it experiences an apparent loss of weight which is exactly equal to the weight of the liquid (or gas) displaced by the body.

$$\mathbf{\text{Apparent Weight } (W') = \text{Real Weight in Air } (W) - \text{Buoyant Force } (F_b)}$$

$$\mathbf{\text{Apparent Loss of Weight} = W - W' = \text{Weight of Displaced Liquid } (V_{\text{displaced}} \cdot \rho_{\text{liquid}} \cdot g)}$$

For an object of density $\rho_{\text{body}}$ placed in a fluid of density $\rho_{\text{liquid}}$:

• Case 1: Sinking (নিমজ্জন): If $\rho_{\text{body}} > \rho_{\text{liquid}}$, Real Weight $W >$ Max Buoyancy $F_b$. The net downward force causes the body to accelerate downward and sink to the bottom (e.g., solid iron nail in water, $\rho_{\text{Fe}} = 7.8\text{ g/cm}^3 > 1.0\text{ g/cm}^3$).
• Case 2: Neutral Floatation (সম্পূর্ণ নিমজ্জিত অবস্থায় ভাসন): If $\rho_{\text{body}} = \rho_{\text{liquid}}$, $W = F_b$. The body floats completely submerged at any depth where it is placed.
• Case 3: Partial Floatation (আংশিক নিমজ্জিত অবস্থায় ভাসন): If $\rho_{\text{body}} < \rho_{\text{liquid}}$, the body sinks only until the weight of fluid displaced equals its total weight ($W = F_b$).
• Scientific Paradox Solved: A solid iron nail sinks because its density ($7.8\text{ g/cm}^3$) exceeds water. However, an ocean liner made of thousands of tons of steel floats because it contains enormous hollow air spaces; its average density (total mass / total enclosed volume) is significantly less than water ($1.0\text{ g/cm}^3$), enabling it to displace a weight of water equal to its own weight.

The envelope of air surrounding Earth exerts immense hydrostatic pressure on all surface objects due to its weight. In 1643, Italian physicist Evangelista Torricelli measured this pressure using a 1-meter long glass tube filled with mercury ($ ext{Hg}$) inverted into a mercury trough.

• The mercury column descended until it stabilized at a vertical height of exactly 76 cm (760 mm) above the trough level at sea level.
• Torricellian Vacuum (টরিসেলির শূন্যস্থান): The empty space above the mercury column in the tube contains only trace mercury vapor and virtually zero air pressure ($P \approx 0$).
• The downward pressure of 76 cm of mercury balances the external atmospheric pressure pushing on the open trough surface.

The standard atmospheric pressure ($1\text{ atm}$) is computed using $P_0 = h \rho g$ for mercury ($\rho_{\text{Hg}} = 13,600\text{ kg/m}^3, g = 9.8\text{ m/s}^2$):

$$P_0 = 0.76\text{ m} \times 13,600\text{ kg/m}^3 \times 9.8\text{ m/s}^2 = \mathbf{1.0129 \times 10^5\text{ N/m}^2} = \mathbf{1.013 \times 10^5\text{ Pa}} = \mathbf{1.013\text{ bar}}$$

Why Mercury over Water? Water density is only $1,000\text{ kg/m}^3$. A water barometer would require a glass tube over $\frac{1.013 \times 10^5}{1000 \times 9.8} \approx \mathbf{10.34\text{ meters}}$ (over 34 feet tall), making it utterly impractical.

Atmospheric pressure variations provide crucial meteorological clues:

• Sudden Sharp Fall in Barometer Reading: Indicates a localized low-pressure zone rapidly created by rising warm air, predicting an approaching severe storm or cyclone.
• Slow Gradual Fall: Indicates increasing humidity and water vapor content (since humid air is lighter than dry air), predicting rain.
• Gradual Steady Rise: Indicates dry, dense air displacing moisture, predicting fair, clear weather.
• Abrupt Spike: Indicates rapid transit of cold air masses, followed by temporary squalls.

A siphon (সাইফন) is an inverted U-shaped tube used to transfer liquid from a higher container over an intervening obstacle into a lower container without tilting either vessel.

• Working Principle: The tube is first primed completely with liquid. At the higher reservoir surface $A$, pressure is $P_0$. At the crest $C$ (height $h_1$ above $A$), pressure is $P_C = P_0 - h_1 \rho g$. At the outlet $D$ (height $h_2$ below $C$), downward hydrostatic pressure causes fluid ejection.
• Because $h_2 > h_1$, the net pressure driving the fluid toward the lower vessel is $\Delta P = (h_2 - h_1) \rho g$. The liquid flows continuously under the influence of atmospheric pressure and gravity.

For a siphon to function successfully:

1. The outlet end must terminate vertically lower than the liquid surface in the upper container ($h_2 > h_1$).
2. The vertical crest height $h_1$ above the upper surface must be strictly less than the barometric height of the liquid ($h_1 < \frac{P_0}{\rho g} \approx 10.3\text{ m}$ for water at sea level). If $h_1 > 10.3\text{ m}$, the liquid column breaks due to cavitation.
3. The siphon tube must be completely airtight; any air leak destroys the continuous pressure gradient.
4. A siphon cannot work in a vacuum because external atmospheric pressure is required to push fluid up the shorter limb.

Heat (তাপ): A form of energy that flows spontaneously from a body at higher temperature to one at lower temperature ($Q$, measured in Joules or Calories, where $1\text{ cal} = 4.184\text{ J} \approx 4.2\text{ J}$).
Temperature (উষ্ণতা): The thermal state of a substance that determines the direction of heat transfer.

Universal Inter-Scale Transformation Formula:
$$\mathbf{\frac{C - 0}{100} = \frac{F - 32}{180} = \frac{K - 273}{100} \implies \frac{C}{5} = \frac{F - 32}{9} = \frac{K - 273}{5}}$$

At $-40^\circ$, both Celsius and Fahrenheit scales register identical readings ($-40^\circ\text{C} = -40^\circ\text{F}$). Absolute Zero is $0\text{ K} = -273.15^\circ\text{C}$.

When two bodies at different temperatures are placed in thermal contact without chemical reaction or heat loss to surroundings: Heat Gained = Heat Lost.

$$\mathbf{Q = m \cdot s \cdot \Delta t}$$

• $m = \text{mass}$, $s = \text{specific heat capacity}$, $\Delta t = \text{temperature variation}$.
• High Specific Heat of Water: Water has an exceptionally high specific heat ($s_{\text{water}} = 1\text{ cal}/(\text{g}\cdot^\circ\text{C}) = 4200\text{ J}/(\text{kg}\cdot\text{K})$). It warms up slowly and cools down slowly. Practical outcomes: Used as coolant in car radiators, hot water bags for medical fomentation, and moderation of coastal climates (Land Breeze & Sea Breeze).

Latent Heat (লীনতাপ): The quantity of heat energy absorbed or liberated by unit mass of a substance to change its physical state at constant temperature.

$$\mathbf{Q = m \cdot L}$$

• Latent Heat of Fusion of Ice ($L_f$): $\mathbf{80\text{ cal/g}}$ ($3.36 \times 10^5\text{ J/kg}$). $1\text{ g}$ of ice at $0^\circ\text{C}$ requires $80\text{ cal}$ of heat to transform into $1\text{ g}$ of water at $0^\circ\text{C}$. This explains why ice cubes cool a drink far more effectively than water at $0^\circ\text{C}$, and why mountain snow melts slowly over months rather than flooding rivers instantly.
• Latent Heat of Vaporization of Water ($L_v$): $\mathbf{537\text{ cal/g}}$ ($2.26 \times 10^6\text{ J/kg}$). $1\text{ g}$ of boiling water at $100^\circ\text{C}$ absorbs $537\text{ cal}$ to become steam at $100^\circ\text{C}$. Consequently, steam causes vastly more severe burns than boiling water at the same temperature because each gram releases 537 additional calories upon condensing on skin.

Evaporation (বাষ্পায়ন): A silent, spontaneous surface phenomenon occurring at all temperatures.
Boiling (স্ফুটন): A rapid, bulk phenomenon occurring only at a fixed temperature (boiling point) where liquid vapor pressure equals external atmospheric pressure.

Evaporative Cooling Principle: High kinetic energy molecules escape the liquid surface, drawing latent heat from the remaining liquid and container. Everyday manifestations:

• Water stored in porous earthen pitchers (মাটির কলসি) remains cool even in scorching summer because water continuously oozes through microscopic pores and evaporates, extracting latent heat from the pitcher.
• Pouring spirit or ether on the hand feels intensely cold.
• Dogs pant with protruding tongues during summer to cool down through saliva evaporation.

Heat propagates via three distinct mechanisms:

• Conduction (পরিবহন): Transfer between adjacent molecules via kinetic collisions without physical displacement of particles (predominant in solids). Davy's Safety Lamp works on wire gauze conductivity.
• Convection (পরিচলন): Transfer through actual bulk motion of fluid particles due to density gradients (liquids and gases). Drives Sea Breeze and Land Breeze.
• Radiation (বিকিরণ): Transmission via electromagnetic waves requiring no intervening medium (how solar heat traverses outer space to reach Earth). Black/dull surfaces are ideal absorbers and emitters; polished shiny surfaces reflect radiation.
• Thermos Flask (Dewar Flask) Construction: Double-walled glass vessel with vacuum between walls (stops conduction and convection), silvered mirror inner surfaces (stops radiation), and insulated cork/plastic stopper (minimizes conduction losses).

When a ray of light passes obliquely from one transparent optical medium to another, it deviates from its original straight trajectory at the interface. This optical bending is called refraction (প্রতিসরণ).

• Rarer to Denser Medium (e.g., Air to Glass): The refracted ray bends toward the normal ($i > r, v_{\text{denser}} < v_{\text{rarer}}$).
• Denser to Rarer Medium (e.g., Glass to Air): The refracted ray bends away from the normal ($i < r$).
• Snell's Law: $\mathbf{\frac{\sin i}{\sin r} = \mu = \frac{c}{v}}$, where $\mu$ is the refractive index of the medium, $c$ is speed of light in vacuum, and $v$ is speed in the medium.
• Normal Incidence ($i = 0^\circ$): The ray passes straight through without deviation ($r = 0^\circ$).

Refraction creates several fascinating optical illusions:

• Bent Pencil in Water: A straight pencil dipped obliquely in water appears broken or bent upward at the water-air boundary due to rays from the submerged portion bending away from the normal into the observer's eye.
• Apparent Shallowness of Ponds: The apparent depth $d'$ of an object at bottom is less than the real depth $d$: $\mathbf{d' = \frac{d}{\mu}}$. For water ($\mu = \frac{4}{3}$), apparent depth is $\frac{3}{4}$ of real depth.
• Advanced Sunrise & Delayed Sunset: Atmospheric refraction curves sunlight over the horizon, extending perceived daylight by approximately 4 minutes daily.

When light travels from an optically denser medium into a rarer medium:

• As angle of incidence $i$ increases, refraction angle $r$ increases toward $90^\circ$.
• Critical Angle (সংকট কোণ, $\theta_c$): The specific angle of incidence in the denser medium for which the angle of refraction in the rarer medium equals exactly $90^\circ$:
  $$\mathbf{\sin \theta_c = \frac{1}{\mu}}$$
• Values: Water $\theta_c \approx 48.6^\circ$, Crown Glass $\approx 42^\circ$, Diamond $\approx 24.4^\circ$.
• Total Internal Reflection: If $i > \theta_c$, no refraction can occur; $100\%$ of the incident light is completely reflected back into the denser medium adhering to reflection laws without energy loss.
• Two Mandatory Conditions for TIR:
  1. Light must travel from an optically denser medium toward a rarer medium.
  2. Angle of incidence must be strictly greater than the critical angle ($i > \theta_c$).

TIR powers both natural wonders and cutting-edge technologies:

• Desert Mirage (মরুভূমির মরীচিকা): Under blistering sun, desert sand heats the bottom air layers, making them rarer while upper air layers remain cooler and denser. Light rays from distant trees curve downward through progressively rarer layers; when $i > \theta_c$, total internal reflection bends rays upward into the observer's eye, creating inverted virtual images that resemble reflections on a water pool.
• Sparkle of Diamonds: Diamond's ultra-low critical angle ($24.4^\circ$) and expertly cut multifaceted geometry cause light entering the gem to undergo multiple internal reflections before exiting, producing dazzling brilliance.
• Endoscopy & Optical Fibers: Flexible glass fibers with high-refractive index core and lower-index cladding transmit light beams over immense distances around tight corners via successive total internal reflections with zero energy dissipation.

A lens is a transparent optical medium bounded by two spherical surfaces or one spherical and one planar surface:

• Convex Lens (উত্তল লেন্স - Converging): Thicker at center, thinner at edges; converges parallel incident rays to a real focus.
• Concave Lens (অবতল লেন্স - Diverging): Thinner at center, thicker at edges; diverges parallel incident rays from a virtual focus.
• Myopia (হ্রস্বদৃষ্টি / Short-Sightedness): Distant objects appear blurred because the elongated eyeball or excessive cornea curvature focuses parallel rays in front of the retina. Correction: Eyeglasses with a concave lens of appropriate focal length.
• Hypermetropia (দীর্ঘদৃষ্টি / Long-Sightedness): Near objects appear blurred because the shortened eyeball focuses near rays behind the retina. Correction: Eyeglasses with a convex lens.
• Least Distance of Distinct Vision (স্পষ্ট দর্শনের ন্যূনতম দূরত্ব): For a healthy adult human eye, $D = \mathbf{25\text{ cm}}$.