Thermodynamics, Waves & Optics
Welcome to the complete guide for Meditaliano Physics. This module covers the most abstract yet heavily tested areas of physics. Unlike Mechanics, which deals with visible objects like balls and cars, this section deals with the behavior of billions of atoms (Thermodynamics), the propagation of energy through space (Waves), and the manipulation of light (Optics).
To master these topics, one must understand the microscopic origins of macroscopic laws. Why does gas pressure exist? Why does a spoon look bent in water? Why does an ambulance siren change pitch? This guide provides the deep theoretical derivations and physical intuition required to answer these questions confidently.
1. Kinetic Theory & Ideal Gases
The Kinetic Molecular Theory is the bridge between the microscopic world of atoms and the macroscopic world we experience (Pressure, Volume, Temperature). We treat gases as "Ideal" to simplify the math. An Ideal Gas assumes:
1. Particles are point masses with negligible volume.
2. There are no intermolecular forces (no attraction/repulsion).
3. Collisions are perfectly elastic (Kinetic energy is conserved).
Figure 1.1: Molecules in random thermal motion colliding with container walls create Pressure.
The Microscopic Origin of Pressure
Pressure is often misunderstood as a static "push". In reality, it is the result of billions of tiny collisions per second. Let's trace the logic from a single particle hitting a wall to the Ideal Gas Law.
Consider a particle of mass $m$ moving with velocity $v_x$ towards a wall. When it hits the wall elastically, it bounces back with velocity $-v_x$. The change in momentum is:
$\Delta p = p_{final} - p_{initial} = (-mv_x) - (mv_x) = -2mv_x$
By Newton's 3rd Law, the wall receives an impulse of $+2mv_x$.
The particle must travel to the opposite wall and back to hit the first wall again. If the box has length $L$, the round-trip distance is $2L$. The time between collisions is:
$\Delta t = \frac{\text{Distance}}{\text{Speed}} = \frac{2L}{v_x}$
Force is the rate of change of momentum (Newton's 2nd Law). For one particle:
$F = \frac{\Delta p}{\Delta t} = \frac{2mv_x}{2L/v_x} = \frac{mv_x^2}{L}$
We sum the force for all $N$ particles. Also, particles move in 3 dimensions ($x, y, z$). On average, $v_x^2 = \frac{1}{3}v^2$. Pressure is Force / Area ($L^2$).
$P = \frac{F_{total}}{A} \implies PV = \frac{1}{3}Nmv_{rms}^2$
Where $k_B$ is the Boltzmann constant ($1.38 \times 10^{-23} J/K$).
Crucial Insight: Temperature is NOT a measure of heat; it is a measure of motion. At the same temperature, heavy molecules (like Oxygen) move slower than light molecules (like Hydrogen), but they possess the exact same average kinetic energy.
Internal Energy of Ideal Gases
For a monatomic ideal gas (like Helium or Neon), the only energy it has is translational kinetic energy. Thus, the total Internal Energy ($U$) is simply the sum of kinetic energies of all $N$ particles:
This equation proves that for an ideal gas, Internal Energy depends only on Temperature. If T is constant (Isothermal), U is constant.
Maxwell-Boltzmann Distribution (Speed of Particles)
As temperature increases, the curve flattens and shifts right. The average speed increases, and the distribution of speeds becomes wider.
Challenge an IMAT Question!
Official Paper: 2024 - Q56
worked solution & explanation
Concept Boyle's Law (Isothermal Process). For a fixed mass of an ideal gas at constant temperature, pressure is inversely proportional to volume ($P \propto 1/V$).
Step 1 Equation: $P_1 \cdot V_1 = P_2 \cdot V_2$.
Step 2 Substitute changed variable: $P_1 \cdot V_1 = P_2 \cdot (3 V_1)$.
Step 3 Solve for $P_2$: $P_2 = P_1 / 3$. The pressure becomes one-third.
Challenge an IMAT Question!
Official Paper: 2022 - Q54
1. The final temperature of the gas is the same as before the change.
2. The final internal energy of the gas is the same as before the change.
3. The final mean kinetic energy of the particles of the gas is the same as before the change.
worked solution & explanation
Concept Ideal Gas Law & Internal Energy principles. Evaluate the overarching state variable (Temperature) first.
| Process | Constant | 1st Law (\Delta U = Q - W) |
|---|---|---|
| Isothermal | Temp ($T$) | \Delta U = 0 \implies Q = W |
| Isobaric | Press ($P$) | \Delta U = Q - P\Delta V |
| Isochoric | Vol ($V$) | W = 0 \implies \Delta U = Q |
| Adiabatic | Q = 0 | \Delta U = -W |
Step 1 Apply $PV = nRT$. New state is $(2P) \times (V/2) = 1 \cdot PV$. Since $PV$ is identical, Temperature $T$ remains perfectly constant. (Statement 1 True).
Step 2 Internal Energy (U) is strictly a function of absolute temperature ($U = \frac{3}{2}nRT$). Constant T means constant U. (Statement 2 True).
Step 3 Mean kinetic energy is directly proportional to absolute temperature ($KE = \frac{3}{2}kT$). Constant T means constant KE. (Statement 3 True).
Challenge an IMAT Question!
Official Paper: 2019 - Q56
worked solution & explanation
Concept Boyle's Law Graphing. An isothermal process means temperature is constant, yielding $P = k / V$.
Step 1 Mathematically, $y = k/x$ produces a rectangular hyperbola (curved line).
Step 2 As volume ($x$) increases, pressure ($y$) decreases, making the gradient strictly negative.
Step 3 As you move to the right (larger V), the curve flattens out, approaching the axis. Thus, the 'steepness' (magnitude) of the negative gradient decreases.
Challenge an IMAT Question!
Official Paper: 2018 - Q59
1. They have an equal mean square velocity.
2. A nitrogen molecule has a greater mean square velocity than an oxygen molecule.
3. A nitrogen molecule has a greater mean kinetic energy than an oxygen molecule.
4. An oxygen molecule has a greater mean kinetic energy than a nitrogen molecule.
worked solution & explanation
Concept Kinetic Theory of Gases. Absolute Temperature is the sole determinant of mean kinetic energy, regardless of chemical identity or mass.
Step 1 Since both gases are at $300\text{ K}$, their mean kinetic energies ($\frac{1}{2}mv^2$) are perfectly identical.
Step 2 Set KEs equal: $\frac{1}{2} m_{O2} (v_{O2})^2 = \frac{1}{2} m_{N2} (v_{N2})^2$.
Step 3 Because Nitrogen ($N_2$) has a smaller mass, its velocity term (mean square velocity) must mathematically be larger to balance the equation.
2. Phase Change & Calorimetry
Thermodynamics begins with the study of heat transfer. A critical concept to understand is that when you add heat energy ($Q$) to a substance, it does one of two things. It never does both simultaneously. It either increases the Kinetic Energy (Temperature) OR it increases the Potential Energy (Phase Change).
A. Changing Temperature
When heat is added within a single phase (e.g., water from 20°C to 80°C), energy goes into vibrating the molecules faster.
B. Changing Phase
Once a substance reaches its melting or boiling point, added heat no longer raises the temperature. Instead, energy goes into breaking the potential bonds holding molecules together.
- $L_f$ (Fusion): Solid $\leftrightarrow$ Liquid. Energy to break the rigid crystal lattice.
- $L_v$ (Vaporization): Liquid $\leftrightarrow$ Gas. Energy to completely sever intermolecular attraction. Note that $L_v \gg L_f$ because gas molecules must be completely separated.
Calorimetry: The Mixing Problem
One of the most common exam questions involves mixing two substances at different temperatures (e.g., dropping hot iron into cold water). In an isolated system (like a perfect thermos), energy is conserved. The heat lost by the hot object must equal the heat gained by the cold object.
Conservation of Energy
$-Q_{lost} = Q_{gained}$
$m_1 c_1 (T_{hot} - T_{final}) = m_2 c_2 (T_{final} - T_{cold})$
Strategy Tip: Always set up the equation as Positive = Positive. Use $(T_{high} - T_{final})$ for the hot side and $(T_{final} - T_{low})$ for the cold side. This avoids sign errors.
Challenge an IMAT Question!
Official Paper: 2023 - Q58
worked solution & explanation
Concept Calorimetry. Total Heat Lost by the hotter substance equals Total Heat Gained by the colder substance.
Step 1 Heat Lost by hot water (M) cooling to $T_2$: $Q_{\text{lost}} = M \cdot c \cdot (T_1 - T_2)$.
Step 2 Heat Gained by ice (m): First melt at $0^\circ\text{C}$ ($m \cdot L_f$), then warm from $0^\circ\text{C}$ to $T_2$ ($m \cdot c \cdot T_2$). $Q_{\text{gained}} = m(L_f + cT_2)$.
Step 3 Equate them: $M \cdot c(T_1 - T_2) = m(L_f + cT_2)$. Isolate m: $m = \frac{Mc(T_1 - T_2)}{L_f + cT_2}$.
Challenge an IMAT Question!
Official Paper: 2022 - Q59
worked solution & explanation
Concept Calorimetry & Power. Combine the heat energy formula $Q = mc\Delta T$ with the power formula $P = Q / t$.
Step 1 Calculate thermal energy required: $Q = 1.20 \times 500 \times (90.0 - 40.0) = 600 \times 50 = 30,000\text{ J}$.
Step 2 Convert time to SI seconds: $5.0\text{ minutes} = 300\text{ seconds}$.
Step 3 Calculate Power (Watts = Joules/second): $P = 30,000 / 300 = 100\text{ W}$.
Challenge an IMAT Question!
Official Paper: 2020 - Q58
worked solution & explanation
Concept Latent Heat formulation. Connect electrical energy supplied to phase-change energy demanded ($E = P \cdot t$ and $E = m \cdot L$).
Step 1 Calculate total electrical energy supplied: $E = 100\text{ W} \times 1600\text{ s} = 160,000\text{ Joules}$.
Step 2 This entire energy was used to vaporize the mass. $E = m \cdot L \implies L = E / m$.
Step 3 Options are in $\text{J/g}$, keep mass in grams: $L = 160,000\text{ J} / 200\text{ g} = 800\text{ J/g}$.
Challenge an IMAT Question!
Official Paper: 2015 - Q59
worked solution & explanation
Concept Specific Heat Formula Algebraic Manipulation.
Step 1 Write standard formula: $Q = m \cdot c \cdot \Delta T$.
Step 2 Isolate specific heat capacity ($c$): $c = \frac{Q}{m \cdot \Delta T}$.
Step 3 Substitute values: $c = \frac{9000}{2.5 \times 4}$.
Challenge an IMAT Question!
Official Paper: 2012 - Q71
worked solution & explanation
Concept Calorimetry Equilibrium Mechanics. Calorimetry strictly relies on the First Law of Thermodynamics: Heat lost = Heat gained.
Step 1 Equilibrium formula: $m_{\text{iron}} \cdot c_{\text{iron}} \cdot \Delta T_{\text{iron}} = m_{\text{water}} \cdot c_{\text{water}} \cdot \Delta T_{\text{water}}$. We absolutely need masses, final temperatures, and water's specific heat.
Step 2 Thermal conductivity dictates *how fast* the heat transfers, but has zero mathematical bearing on the final equilibrium state or total energy exchanged.
Challenge an IMAT Question!
Official Paper: 2012 - Q72
1. The substance becomes more disordered.
2. The wax takes in heat but its temperature stays the same.
3. Bonds between the carbon and hydrogen atoms are broken.
worked solution & explanation
Concept Phase Change Thermodynamics and Chemistry. Differentiate between intermolecular forces and intramolecular covalent bonds.
Step 1 Statement 1 (True): Melting transitions a solid to a liquid, increasing entropy and disorder.
Step 2 Statement 2 (True): During phase change, inputted thermal energy strictly serves as Latent Heat to overcome intermolecular forces, halting temperature rise.
Step 3 Statement 3 (False): Melting overcomes weak *intermolecular* Van der Waals forces. It does NOT break the strong *intramolecular* covalent C-H bonds.
3. Heat Transfer Mechanisms
The Second Law of Thermodynamics (Clausius Statement) dictates that heat spontaneously flows from regions of High Temperature to Low Temperature until equilibrium is reached. Nature has three distinct mechanisms to achieve this.
| Type | Detailed Mechanism | Key Physics |
|---|---|---|
| Conduction | Molecular Dominoes. This is the transfer of energy through direct physical contact. Fast-vibrating atoms bump into slower neighbors, transferring kinetic energy. In metals, "free electrons" zip through the lattice, making conduction very efficient. |
Rate $\propto \frac{k A \Delta T}{L}$ $k$: Thermal Conductivity $A$: Area, $L$: Thickness |
| Convection | Fluid Transport. This involves the bulk movement of the fluid itself. As a fluid heats up, it expands and becomes less dense. Buoyant forces push the hot fluid up, while cold, denser fluid sinks to replace it, creating a circulation current. | Requires Fluid + Gravity. |
| Radiation | Photon Emission. All objects with a temperature above absolute zero emit electromagnetic waves (infrared). This is caused by the acceleration of charged particles within atoms. Unlike conduction/convection, this does not require a medium. |
Stefan-Boltzmann Law: $P = \sigma A e T^4$ Doubling T increases Power by 16x! |
Figure 3.1: Heat transfer by convection showing how hot, less dense fluid rises and cold, denser fluid sinks to replace it.
4. The First Law of Thermodynamics
The First Law is essentially the Law of Conservation of Energy applied to heat and work. It states that energy cannot be created or destroyed, only transferred. The change in a system's internal energy is equal to the heat added to it minus the work done by it.
$\Delta U$: Change in Internal Energy | $Q$: Heat Added | $W$: Work Done BY Gas
Sign conventions are the most common source of errors in physics problems. You must memorize these:
$\Delta U$ (Internal Energy)
This represents the total kinetic energy stored in the gas atoms. It is directly linked to Temperature.
- (+) Temp Increases ($T_f > T_i$)
- (-) Temp Decreases ($T_f < T_i$)
- (0) Isothermal ($T_f = T_i$)
$Q$ (Heat)
Energy transferred solely due to temperature difference.
- (+) Heat ENTERS (Endothermic)
- (-) Heat LEAVES (Exothermic)
- (0) Adiabatic (Insulated)
$W$ (Work)
Mechanical energy transfer via volume change ($W = P\Delta V$).
- (+) Expansion (Gas pushes piston)
- (-) Compression (Piston pushes gas)
- (0) Isochoric (Rigid Box)
Be careful! In Chemistry, the law is often written as $\Delta U = Q + W$. This is because chemists define Work as "Work done ON the system". In Physics, we care about engines (work output), so we define Work as "Work done BY the system". The Physics convention ($-W$) means when a gas expands, it LOSES energy to do work.
Challenge an IMAT Question!
Official Paper: 2017 - Q59
worked solution & explanation
Concept First Law of Thermodynamics: $\Delta U = Q - W$. (Change in Internal Energy = Heat added - Work done BY system).
Step 1 Substitute values: $\Delta U = 3500\text{ J (heat)} - 3500\text{ J (work)} = 0$.
Step 2 Since the change in internal energy is zero, the absolute temperature of the ideal gas must have remained perfectly constant. This is 'isothermal'.
5. Thermodynamic Processes
We analyze thermodynamic cycles using Pressure-Volume (PV) diagrams. The most important rule to remember for PV diagrams is: Work ($W$) is the Area Under the Curve.
Isobaric
Isochoric
Isothermal
Adiabatic
| Process | Constant | 1st Law Analysis | Detailed Description |
|---|---|---|---|
| Isobaric | Pressure ($P$) | $\Delta U = Q - P\Delta V$ | Horizontal line. To keep pressure constant while volume increases, the gas must be heated significantly. Some heat does work (pushing piston), and the rest raises the temperature. |
| Isochoric | Volume ($V$) | $\Delta U = Q$ | Vertical line. Think "Pressure Cooker". Since the piston doesn't move ($dV=0$), no Work is done. 100% of added heat goes directly into raising Internal Energy. This is the most efficient way to raise Temperature. |
| Isothermal | Temp ($T$) | $Q = W$ | Hyperbola ($P \propto 1/V$). This process happens slowly. As the gas expands, it tends to cool, but heat is added from a reservoir to keep T constant. Since T is constant, $\Delta U = 0$. All input heat becomes Work. |
| Adiabatic | Heat ($Q=0$) | $\Delta U = -W$ | Steep Curve. This happens very fast (like a piston firing) or in an insulated box. No time for heat exchange. If gas expands, it does work using its own internal energy, causing $T$ to crash. If compressed, $T$ skyrockets (how Diesel engines ignite fuel). |
Challenge an IMAT Question!
Official Paper: 2023 - Q57
worked solution & explanation
Concept Gay-Lussac's Law (Isochoric Process). At constant volume, pressure is directly proportional to absolute Kelvin temperature ($P \propto T$).
Step 1 Convert initial temperature to Kelvin: $T_1 = 25 + 273 = 298\text{ K}$. (The initial isothermal pull doesn't change this).
Step 2 Because pressure is exactly halved, temperature must halve: $T_2 = 298 / 2 = 149\text{ K}$.
Step 3 Convert back to Celsius: $149\text{ K} - 273 = -124^\circ\text{C}$.
6. Engines & Entropy
A Heat Engine is a device that operates in a cycle to convert Heat into Work. Think of a steam engine or a car engine.
The Second Law of Thermodynamics (Kelvin-Planck statement) tells us a hard truth: It is impossible to build a 100% efficient engine. You cannot simply extract heat from a source and turn it all into work. You must dump some waste heat into a cold reservoir (the exhaust).
Entropy is a measure of "disorder" or the number of possible microscopic configurations.
Mathematically, $\Delta S = Q/T$.
The Entropy of the Universe always increases. This explains the "Arrow of Time". You can scramble an egg (increasing entropy), but you can never unscramble it. Energy naturally spreads out.
Energy flows down from Hot to Cold, diverting some energy as Work along the way.
Challenge an IMAT Question!
Official Paper: 2011 - Q72
worked solution & explanation
Concept Entropy and Reversibility. Entropy generation is driven by irreversible processes: friction, chaotic collisions, heat transfer, and phase changes.
Step 1 Evaporation, rapid electroplating, bouncing, and terminal velocity all involve immense kinetic energy dissipation into chaotic heat, generating massive entropy.
Step 2 A satellite orbiting in the vacuum of space experiences virtually zero air resistance. Its mechanical energy exchange is nearly perfectly reversible, generating effectively zero entropy.
7. The Nature of Waves
A wave is a disturbance that carries Energy, not matter, through a medium (or vacuum). Imagine a stadium wave: the people (medium) only stand up and sit down (oscillate), but the wave (energy) travels around the stadium.
velocity ($m/s$) = frequency ($Hz$) $\times$ wavelength ($m$)
- Frequency ($f$) is determined by the SOURCE. It never changes as the wave travels.
- Velocity ($v$) is determined by the MEDIUM. It changes if the wave enters water/glass/etc.
Types of Waves
Figure 7.1: Transverse waves oscillate perpendicular to motion. Longitudinal waves oscillate parallel to motion.
Particle oscillation is Perpendicular ($90^\circ$) to the direction of energy transfer.
- Light (Electromagnetic Waves)
- Guitar Strings
- Surface water waves
- Can be Polarized (Only transverse waves can be polarized)
Particle oscillation is Parallel to the direction of energy transfer. Creates regions of Compression and Rarefaction.
- Sound Waves
- Ultrasound
- Earthquake P-waves
- Cannot be Polarized
The Electromagnetic Spectrum
Figure 7.2: The Electromagnetic Spectrum. High Frequency = High Energy = Short Wavelength.
Light is a transverse wave composed of oscillating Electric and Magnetic fields. It requires no medium. In a vacuum, all EM waves travel at $c = 3 \times 10^8 m/s$. The energy of a photon is given by $E = hf$.
8. Sound & The Doppler Effect
Sound is a pressure wave. It relies on the collision of particles to propagate. Therefore, sound travels fastest in stiff, dense materials where atoms are tightly packed and interact strongly.
Speed Order: Solids ($~5000m/s$) > Liquids ($~1500m/s$) > Gases ($~340m/s$).
The Doppler Effect
The Doppler effect is the apparent change in frequency of a wave due to relative motion between source and observer. It does not change the actual frequency of the source. It only changes how frequently the wavefronts hit your ear.
Figure 8.1: Compression of wavefronts in the direction of motion causes higher pitch (Frequency Up, Wavelength Down).
$v$: Speed of sound | $v_{obs}$: Speed of Observer | $v_{source}$: Speed of Source
The formula has four sign choices. To simplify, just remember:
- If motion is TOWARD the other object, use the TOP sign.
- If motion is AWAY from the other object, use the BOTTOM sign.
Conceptual Scenarios
| Scenario | Physical Mechanism | Result |
|---|---|---|
| Source moves TOWARD (Ambulance approaches) |
The source "chases" its own waves. Each new wavefront is emitted closer to the previous one, squashing the wavelength ($\lambda \downarrow$). | Pitch Up ($f \uparrow$) |
| Source moves AWAY (Ambulance leaves) |
The source runs away from its waves. Each new wavefront is emitted further back, stretching the wavelength ($\lambda \uparrow$). | Pitch Down ($f \downarrow$) |
| Observer runs TOWARD | The waves don't change, but you run into them faster. You intercept more wavefronts per second. | Pitch Up ($f \uparrow$) |
9. Interference & Standing Waves
Superposition Principle: When two waves meet, they don't bounce off; they pass through each other. At the point of overlap, their displacements add up algebraically.
Figure 9.1: Constructive (In-phase) vs Destructive (Out-of-phase) Interference.
| Type | Condition (Path Diff) | Result |
|---|---|---|
| Constructive | $n\lambda$ (Integer) | Peaks align with Peaks. Amplitude adds up ($A_{total} = 2A$). Creates bright light or loud sound. |
| Destructive | $(n + 0.5)\lambda$ (Half-Int) | Peaks align with Troughs. They cancel out ($A_{total} = 0$). Creates darkness or silence. |
Standing Waves (Resonance)
When a wave reflects back and forth within a confined space (like a guitar string or flute), the interfering waves can create a stationary pattern called a Standing Wave.
- Node (N): Point of zero vibration (Destructive interference).
- Antinode (A): Point of max vibration (Constructive interference).
Strings are fixed at both ends (Nodes). Open pipes are open at both ends (Antinodes). Both follow the same harmonic series.
for n = 1, 2, 3...
Closed at one end (Node) and open at the other (Antinode). A Node-Antinode pair is only 1/4 of a wave. This only supports ODD harmonics.
for n = 1, 3, 5...
10. Reflection & Mirrors
Geometric optics approximates light as rays traveling in straight lines. The key to solving mirror problems is mastering the Ray Diagrams and the Sign Convention.
$f$: focal length | $d_o$: object dist | $d_i$: image dist | $M$: Magnification
Ray Tracing: Concave vs Convex
- Concave Mirror: $f$ is Positive. Can form Real (inverted) or Virtual (upright) images.
- Convex Mirror: $f$ is Negative. ALWAYS forms Virtual, Upright, Smaller images (like a car side mirror).
- Real Images: $d_i$ is Positive. Image is Inverted.
- Virtual Images: $d_i$ is Negative. Image is Upright.
Challenge an IMAT Question!
Official Paper: 2012 - Q74
Network 1: All 3 in series.
Network 2: All 3 in parallel.
Network 3: 2 in parallel, connected in series with the 3rd.
Which of the following shows the order of increasing capacitance (smallest first)?
worked solution & explanation
Concept Capacitor Addition Logic. Note: Capacitor addition rules are the exact inverse of resistor addition rules.
Step 1 Network 1 (Series): Capacitors in series decrease total capacitance. $\frac{1}{C_{\text{eq}}} = \frac{1}{C} + \frac{1}{C} + \frac{1}{C} \implies C_{\text{eq}} = \frac{C}{3} = 0.33C$. (Smallest)
Step 2 Network 2 (Parallel): Capacitors in parallel simply add up. $C_{\text{eq}} = C + C + C = 3C$. (Largest)
Step 3 Network 3 (Hybrid): The parallel pair makes $2C$. This $2C$ is in series with $C$. Use product over sum: $C_{\text{eq}} = \frac{2C \cdot C}{2C + C} = \frac{2C^2}{3C} = 0.67C$. (Middle)
Step 4 Order from smallest to largest: 1, 3, 2.
11. Refraction & TIR
Refraction is the bending of light caused by a change in speed when entering a new medium. Imagine a car driving from pavement (fast) into mud (slow) at an angle. The wheel that hits the mud first slows down, causing the car to pivot (bend) into the mud.
Vacuum $n=1$, Water $n=1.33$, Glass $n=1.5$.
What Changes?
- Speed ($v$): Changes. Slower in higher $n$.
- Wavelength ($\lambda$): Changes. $\lambda_n = \lambda_{vacuum} / n$. Wavelength gets shorter in dense medium.
- Frequency ($f$): CONSTANT. Frequency depends on the source and never changes during refraction.
Total Internal Reflection (TIR)
When light tries to leave a dense medium (Water $\to$ Air), it bends away from the normal. If the angle is steep enough, the refracted ray is bent $90^\circ$ along the surface. Beyond this Critical Angle, the light cannot escape and reflects back completely. This is the principle behind Fiber Optics.
Dispersion (Prism)
Violet light has a higher index $n$ than Red, so it slows down more and bends more.
12. Lenses & Image Formation
Figure 12.1: Ray tracing for Converging (Convex) and Diverging (Concave) Lenses.
Lenses work by refraction, but the mathematics is nearly identical to mirrors. The main difference is the "Virtual" side. For mirrors, light reflects, so the "Real" side is in front. For lenses, light passes through, so the "Real" side is behind.
Vision Defects
Problem: The eyeball is too long or the lens is too strong. Light focuses in front of the retina.
Symptom: Can see near, but far is blurry.
Solution: Diverging (Concave) lens to spread light out before entering eye.
Problem: The eyeball is too short or lens is too weak. Light focuses behind the retina.
Symptom: Can see far, but near is blurry.
Solution: Converging (Convex) lens to help focus light sooner.
Challenge an IMAT Question!
Official Paper: 2020 - Q59
1. Incident rays travelling parallel to the principal axis always pass through $F$ after reflection.
2. Incident rays passing through $F$ always travel parallel to the principal axis after reflection.
3. The image formed is always inverted.
4. The image formed is always real.
5. The image formed is always larger than the object.
worked solution & explanation
Concept Ray Tracing Rules for Parabolic Concave Mirrors.
Step 1 Statement 1 (True): Any ray travelling parallel to the principal axis reflects directly through the focal point (F).
Step 2 Statement 2 (True): Due to optical reversibility, any ray passing through the focal point reflects strictly parallel to the principal axis.
Step 3 Statements 3 & 4 (False): If an object is placed between F and the mirror, the reflected rays diverge, forming a Virtual, Upright, and Magnified image.