SNC2D · Exam review

Science Exam Review

A practice exam with questions from all 4 units, then the key facts from every lesson, unit by unit. For a deeper look at one unit, open its test review.

Unit test reviews

Practice exam

32 questions, the same number from each unit. Each one shows the lesson it comes from.

Unit 1: Plant and Animal Cells and the Microscope
1
Which structure is found in plant cells but not in animal cells?
Unit 1: The Cell Cycle and Mitosis
2
A cube-shaped cell has sides 4 µm long. What is its surface-area-to-volume ratio (surface area ÷ volume, in units of 1/µm)?
Unit 1: Cancer: When Cell Division Goes Wrong
3
What is the term for the spread of cancer cells through the blood or lymph to form new tumours in other parts of the body?
Unit 1: Cell Specialization, Differentiation and Stem Cells
4
Why are induced pluripotent stem cells (iPSCs) seen as a possible way around one ethical concern?
Unit 1: The Digestive System
5
Put these organs in the order food passes through them.
1. 1Large intestine
2. 2Small intestine
3. 3Rectum
4. 4Mouth
5. 5Esophagus
6. 6Stomach
Unit 1: The Circulatory and Respiratory Systems
6
Match each part of the blood to its job.
Red blood cells
White blood cells
Platelets
Plasma
Unit 1: Plant Tissues, Organs and Systems
7
Put the steps in the path of water through a plant in order.
1. 1Water evaporates from a mesophyll cell into an air space
2. 2Water reaches a vein in the leaf
3. 3Water vapour diffuses out through a stomate
4. 4Water enters a root hair cell from the soil
5. 5Water enters the xylem in the root
6. 6Water travels up the xylem in the stem
Unit 1: Medical Imaging, Public Health and Ethics
8
Why is ultrasound, rather than CT, used to check a fetus during pregnancy?
Unit 2: Naming and Writing Formulas for Ionic Compounds
9
Which ion does a magnesium atom form?
Unit 2: Polyatomic Ions, Molecular Compounds and Acids
10
What is the formula of sodium hydroxide?
Unit 2: Evidence of Chemical Change and Conservation of Mass
11
Why does the measured mass of steel wool increase when it burns in an open dish?
Unit 2: Word Equations and Balanced Chemical Equations
12
Balance $Fe + O_{2} \to Fe_{2} O_{3}$ . What coefficient goes in front of Fe?
Unit 2: Synthesis and Decomposition Reactions
13
Water is decomposed by electrolysis: $2 H_{2} O \to 2 H_{2} + O_{2}$ . If 40 mL of oxygen gas is collected, about how many millilitres of hydrogen gas are collected at the same time and conditions?
mL
Unit 2: Single Displacement, Double Displacement and Combustion
14
Balance the complete combustion of butane: $C_{4} H_{10} + O_{2} \to CO_{2} + H_{2} O$ , using the lowest whole numbers. What coefficient goes in front of $CO_{2}$ ?
Unit 2: Acids, Bases, pH and Indicators
15
Which is the safe way to find out whether an unknown liquid in a lab is an acid?
Unit 2: Neutralization and Reactions in the Environment
16
Match each environmental problem to a chemical solution.
An acidified lake
Sulfur dioxide in smokestack gases
Algae blooms fed by phosphates
Cyanide in gold mine wastewater
Unit 3: Weather, Climate and Earth's Climate System
17
Which statement describes climate rather than weather?
Unit 3: Heat Transfer in the Atmosphere and Hydrosphere
18
How does energy from the Sun reach Earth?
Unit 3: The Natural and Anthropogenic Greenhouse Effect
19
Put the steps of the greenhouse effect in order.
1. 1Greenhouse gases re-emit infrared, part of it back toward the surface
2. 2Greenhouse gases absorb some of the infrared
3. 3The warm surface emits longwave infrared radiation
4. 4Shortwave sunlight passes through the atmosphere
5. 5The surface absorbs sunlight and warms
Unit 3: Greenhouse Gases: Sources, Sinks and the Carbon Cycle
20
Which of these is a carbon sink?
Unit 3: Evidence of Past and Present Climate Change
21
Which observation helps rule out the Sun as the main cause of recent warming?
Unit 3: Oceans, Water and Climate Patterns
22
Put the ice-albedo feedback loop in order, starting from the initial warming.
1. 1Temperature rises further
2. 2Albedo decreases, so more sunlight is absorbed
3. 3Darker ocean and land are exposed
4. 4Global temperature rises
5. 5Snow and sea ice melt
Unit 3: Ozone Depletion, Ground-Level Ozone and Smog
23
What is the name of Canada's 1 to 10+ scale for reporting the health risk from air pollution? (Acronym or full name.)
Unit 3: Impacts of Climate Change and How We Respond
24
Which of these is a real effect of climate change on Inuit communities?
Unit 4: What Light Is: The Electromagnetic Spectrum and Sources of Light
25
Which list puts these waves in order of increasing frequency?
Unit 4: Rays, the Laws of Reflection and Plane Mirrors
26
Put the steps for locating the image of a point in a plane mirror in order.
1. 1Mark the image where the dashed extensions cross
2. 2Extend the reflected rays backward behind the mirror as dashed lines
3. 3Draw each reflected ray so that the angle of reflection equals the angle of incidence
4. 4Draw two rays from the object point to the mirror
5. 5Draw the normal at each point of incidence
Unit 4: Concave and Convex Mirrors with Ray Diagrams
27
An object starts far from a concave mirror and moves steadily toward F. Sort the real image's size, from first to last.
1. 1Same size as the object
2. 2Very large and very far away
3. 3Larger than the object
4. 4Much smaller than the object
Unit 4: Refraction, Index of Refraction and the Speed of Light
28
Find the speed of light in diamond ( $n = 2.42$ ) in units of $1 0^{8} m/s$ , to 2 decimal places.
× 10⁸ m/s
Unit 4: Snell's Law
29
Sort the steps for finding a refracted angle with Snell's law.
1. 1Check that the ray bent the correct way
2. 2Take the inverse sine to get $θ_{2}$
3. 3Substitute and calculate the value of $sin θ_{2}$
4. 4Identify medium 1 (where the light comes from) and medium 2
5. 5Rearrange to $sin θ_{2} = \frac{n _{1} sin θ _{1}}{n _{2}}$
Unit 4: Converging and Diverging Lenses with Ray Diagrams
30
Which lens is thicker in the middle than at its edges?
Unit 4: The Thin Lens Equation and Magnification
31
An object is $45.0 cm$ from a converging lens with $f = 15.0 cm$ . Find the image distance in cm, to 1 decimal place.
cm
Unit 4: The Eye, Vision Correction and Optical Devices
32
What is the name of the eye's process of changing the shape of its lens to focus on objects at different distances?

Key facts by unit

Unit 1: Tissues, Organs & Systems of Living Things

Plant and Animal Cells and the Microscope

Cell theory: all living things are made of cells, the cell is the basic unit of life, and cells come only from existing cells.
Of the two, only plant cells have a cell wall, chloroplasts and a large central vacuole; animal cells have small vacuoles, and lysosomes are found mainly in animal cells.
Mitochondria release energy by cellular respiration; chloroplasts capture light energy by photosynthesis; ribosomes make proteins.
Total magnification = ocular × objective, for example 10× × 40× = 400×.
Field of view at high power = field of view at low power × (low magnification ÷ high magnification).
Estimated cell size = field of view diameter ÷ number of cells that fit across it; 1 mm = 1000 µm.

The Cell Cycle and Mitosis

The cell cycle: interphase (growth and DNA copying), then mitosis (prophase, metaphase, anaphase, telophase), then cytokinesis.
Prophase: chromosomes condense and the nuclear membrane breaks down. Metaphase: chromosomes line up at the equator. Anaphase: sister chromatids are pulled apart. Telophase: two nuclei re-form.
Mitosis makes two daughter cells genetically identical to the parent with the same chromosome number (46 in most human body cells).
Cells divide for growth, repair and replacement, and to keep a high surface-area-to-volume ratio.
Plant cells form a cell plate during cytokinesis; animal cells form a cleavage furrow.
Time in a stage = (cells in that stage ÷ total cells) × total cycle time.

Cancer: When Cell Division Goes Wrong

Cancer is a group of many diseases in which cells divide uncontrollably, caused by mutations in genes that control the cell cycle.
Normal cells obey checkpoints, contact inhibition and programmed cell death; cancer cells escape these controls.
Benign tumours stay in one place; malignant tumours invade nearby tissue and can metastasize through blood or lymph.
Mitotic index = (cells in mitosis ÷ total cells) × 100%; it is usually higher in tumour tissue.
Major risk factors include tobacco smoke, UV radiation, HPV, radon, asbestos and alcohol.
Treatments: surgery, radiation, chemotherapy, immunotherapy and targeted drugs; screening finds cancer early.

Cell Specialization, Differentiation and Stem Cells

Differentiation: a cell becomes specialized by using only the instructions it needs for one job; its structure then fits its function.
Stem cells are unspecialized cells that can self-renew and differentiate into specialized cells.
Embryonic stem cells and iPSCs are pluripotent (can become almost any cell type); adult stem cells are more limited.
Meristematic cells at root and shoot tips (and in the cambium) let plants grow throughout their lives.
Regeneration is the regrowth of lost parts; it is extensive in planarians, salamanders and many plants but limited in humans.
McCulloch and Till (Toronto, early 1960s) gave the first clear evidence of stem cells.

From Cells to Systems in Animals

Levels of organization: cell → tissue → organ → organ system → organism.
A tissue is a group of similar cells doing one job; an organ is made of two or more tissue types.
The four animal tissue types are epithelial, connective, muscle and nervous.
Muscle tissue comes in three kinds: skeletal (voluntary), smooth (involuntary, in hollow organs) and cardiac (involuntary, heart only).
Blood, bone, cartilage, tendons and fat are all connective tissues.
Organ systems depend on each other: for example, the respiratory system brings in oxygen and the circulatory system delivers it to cells.

The Digestive System

Mechanical digestion (chewing, churning, emulsifying) increases surface area; chemical digestion uses enzymes to break molecules into smaller ones.
Starch digestion begins in the mouth (amylase), protein digestion in the stomach (pepsin), and most digestion is completed in the small intestine.
Bile from the liver emulsifies fat; it is not an enzyme.
Villi and microvilli give the small intestine a huge surface area for absorption; nutrients pass into capillaries in each villus.
The large intestine absorbs much of the remaining water and forms feces.
Surface area of a cube = 6 × side²; cutting food into smaller pieces increases total surface area.

The Circulatory and Respiratory Systems

The heart has four chambers; the right side pumps blood to the lungs and the left side pumps it to the body (double circulation).
Arteries carry blood away from the heart, veins carry it back, and capillaries (walls one cell thick) are where materials are exchanged.
Red blood cells carry oxygen bound to hemoglobin; white blood cells fight infection; platelets help clotting; plasma carries dissolved materials.
Air path: nasal cavity → pharynx → larynx → trachea → bronchi → bronchioles → alveoli.
Diffusion moves particles from higher to lower concentration; oxygen diffuses from alveoli into capillaries and carbon dioxide diffuses out.
Cardiac output = heart rate × stroke volume.

Plant Tissues, Organs and Systems

Plant tissues: dermal (protection), ground (photosynthesis, storage), vascular (transport) and meristematic (new cells).
The root system anchors the plant and absorbs water and minerals; the shoot system (stems, leaves, flowers) photosynthesizes, supports and reproduces.
Xylem carries water and minerals upward from the roots; phloem carries sugars from the leaves to wherever they are needed, up or down.
Leaf layers: cuticle, upper epidermis, palisade mesophyll, spongy mesophyll, veins, lower epidermis with stomata and guard cells.
Transpiration is water loss from leaves through the stomata; it pulls water up the xylem.
Stomatal density = number of stomata ÷ field-of-view area, where area = π × radius².

Medical Imaging, Public Health and Ethics

X-rays and CT use ionizing radiation; dense tissue such as bone absorbs X-rays. CT builds cross-section slices from many X-ray images.
MRI uses a strong magnet and radio waves acting on hydrogen nuclei; it shows soft tissue in great detail with no ionizing radiation.
Ultrasound times echoes of high-frequency sound: depth = speed × time ÷ 2, with sound travelling about 1540 m/s in soft tissue.
Public health strategies include cancer screening, vaccines (HPV, MMR) and education programs.
Community immunity protects people who cannot be vaccinated; measles needs about 95% of people to be immune.
Transplants, cloning and stem cells raise ethical questions; a balanced analysis weighs benefits, risks and values.

Unit 2: Chemical Reactions

Naming and Writing Formulas for Ionic Compounds

Metals lose electrons to form positive ions (cations); non-metals gain electrons to form negative ions (anions) whose names end in -ide.
Usual charges by group: 1 → 1+, 2 → 2+, 13 → 3+, 15 → 3−, 16 → 2−, 17 → 1−.
In a formula the total positive and negative charge add to zero; write the metal first and use the lowest whole-number ratio.
A Roman numeral in a name gives the charge of one metal ion, e.g. iron(III) means $Fe^{3 +}$ ; use it only for multivalent metals.
Name a binary ionic compound as metal name + non-metal root with -ide, e.g. $CaCl_{2}$ is calcium chloride.

Polyatomic Ions, Molecular Compounds and Acids

A polyatomic ion is a charged group of atoms that acts as one unit, e.g. nitrate $NO_{3}^{-}$ , sulfate $SO_{4}^{2 -}$ , ammonium $NH_{4}^{+}$ .
Use brackets when a formula needs more than one polyatomic ion: $Ca (OH)_{2}$ , $(NH_{4})_{2} SO_{4}$ .
Molecular compounds (non-metals only) use prefixes: mono, di, tri, tetra, penta, hexa; never put mono on the first element.
Binary acids: hydro- + root + -ic acid, e.g. HCl(aq) hydrochloric acid.
Oxyacids: -ate ion → -ic acid ( $H_{2} SO_{4}$ sulfuric), -ite ion → -ous acid ( $H_{2} SO_{3}$ sulfurous).

Evidence of Chemical Change and Conservation of Mass

A chemical change produces new substances; a physical change does not.
Evidence of chemical change: colour change, gas produced, precipitate formed, energy (heat or light) given off or absorbed, new odour.
Gas tests: hydrogen pops with a burning splint, oxygen relights a glowing splint, carbon dioxide turns limewater milky.
Law of conservation of mass: total mass of reactants = total mass of products.
Mass seems to change only in open systems, when a gas escapes or is taken in from the air.

Word Equations and Balanced Chemical Equations

Word equation (names) → skeleton equation (formulas) → balanced equation (coefficients added).
A balanced equation has the same number of atoms of each element on both sides, because atoms are conserved.
Balance by changing coefficients only; changing a subscript changes the substance.
A coefficient multiplies every atom in the formula after it: $2 Ca (OH)_{2}$ has 2 Ca, 4 O and 4 H.
Diatomic elements: $H_{2}$ , $N_{2}$ , $O_{2}$ , $F_{2}$ , $Cl_{2}$ , $Br_{2}$ , $I_{2}$ .

Synthesis and Decomposition Reactions

Synthesis: two or more reactants form one product, A + B → AB.
Decomposition: one reactant breaks into two or more products, AB → A + B.
Metal + non-metal synthesis gives an ionic compound whose formula comes from the ion charges.
Metal oxide + water → base; non-metal oxide + water → acid.
Decomposition usually needs added energy; using electricity is called electrolysis.

Single Displacement, Double Displacement and Combustion

Single displacement: A + BC → AC + B; it happens only if A is above the element it replaces in the activity series.
Metals above hydrogen release $H_{2}$ from acids; the halogen order is $F_{2} > Cl_{2} > Br_{2} > I_{2}$ .
Double displacement: AB + CD → AD + CB; it happens when a precipitate, a gas or water forms.
Complete combustion of a hydrocarbon: $C_{x} H_{y} + O_{2} \to CO_{2} + H_{2} O$ .
Incomplete combustion (limited oxygen) also produces carbon monoxide and soot.

Acids, Bases, pH and Indicators

Acids release $H^{+}$ ions in water; bases release $OH^{-}$ ions (Arrhenius definitions).
pH < 7 is acidic, pH = 7 is neutral, pH > 7 is basic.
Each pH unit is a factor of 10: a difference of $n$ pH units means $1 0^{n}$ times more acidic or basic.
Litmus: blue → red in acid, red → blue in base. Phenolphthalein: colourless in acid, pink in base.
Acids react with active metals to make hydrogen gas and with carbonates to make carbon dioxide.

Neutralization and Reactions in the Environment

Neutralization: acid + base → salt + water, e.g. $HCl + NaOH \to NaCl + H_{2} O$ .
The key change is $H^{+} + OH^{-} \to H_{2} O$ ; the salt is made of the base's cation and the acid's anion.
Acid + carbonate → salt + water + carbon dioxide (used in antacids, spill cleanup and liming lakes).
Acid rain forms when $SO_{2}$ and nitrogen oxides react with water and oxygen in the air to make acids.
Scrubbers use limestone or lime to capture $SO_{2}$ from smokestacks as calcium sulfate.

Unit 3: Climate Change

Weather, Climate and Earth's Climate System

Weather is the short-term state of the atmosphere; climate is the long-term average and range, normally over 30 years.
The climate system: atmosphere, hydrosphere, cryosphere, lithosphere and biosphere, powered by energy from the Sun.
Albedo is the fraction of sunlight reflected (0 to 1); anthropogenic means caused by humans; a heat sink stores heat with little temperature change.
Local climate depends on latitude, nearness to water, ocean currents, prevailing winds, elevation and mountain barriers.
Köppen groups: A tropical, B dry, C temperate, D continental, E polar. Most of Ontario is D.
Ontario's ecozones: Mixedwood Plains, Boreal Shield and Hudson Plains.

Heat Transfer in the Atmosphere and Hydrosphere

Heat flows from warmer to cooler matter by radiation (waves, no medium needed), conduction (contact) or convection (moving fluid).
The Sun heats the surface by radiation; the surface heats the air by conduction; convection carries the heat upward.
Water's specific heat capacity, about 4.18 J/(g·°C), is roughly five times that of sand, so water warms and cools slowly.
$Q = m c Δ T$ : for the same energy and mass, a substance with a larger $c$ changes temperature less.
Wind blows from high pressure to low pressure; sea breezes blow from water to land by day and land breezes from land to water at night.
Over Canada the prevailing winds are westerlies, and weather usually moves from west to east.

The Natural and Anthropogenic Greenhouse Effect

Sunlight arrives as shortwave radiation; Earth's surface gives off longwave infrared radiation.
Earth's average albedo is about 0.30: about 30% of incoming sunlight is reflected to space.
Greenhouse gases (H₂O, CO₂, CH₄, N₂O, O₃, halocarbons) absorb infrared and re-emit part of it back toward the surface.
The natural greenhouse effect raises Earth's average temperature from about −18 °C to about 15 °C.
Human emissions have raised CO₂ from about 280 ppm to over 420 ppm, strengthening the greenhouse effect and warming Earth.
Reflected energy = albedo × incoming energy; absorbed energy = (1 − albedo) × incoming energy.

Greenhouse Gases: Sources, Sinks and the Carbon Cycle

A source releases a greenhouse gas; a sink removes and stores it. Concentration rises when sources exceed sinks.
Main human sources: fossil fuels and cement (CO₂), livestock, landfills and fossil fuel leaks (CH₄), fertilizers (N₂O), refrigerants (halocarbons).
GWP compares warming per tonne with CO₂ over 100 years: CO₂ = 1, CH₄ ≈ 28, N₂O ≈ 270, some halocarbons thousands.
$CO_{2} e = mass of gas \times GWP$
About half of human CO₂ emissions stay in the air; the rest is taken up roughly equally by oceans and land.
Canada: about 694 Mt CO₂e in 2023, about 1.5% of world emissions, but among the highest per person.

Evidence of Past and Present Climate Change

Proxies (ice cores, tree rings, lake and ocean sediments, fossils) record past climate; ice-core bubbles preserve samples of ancient air.
Natural factors: plate tectonics, uplift and weathering, orbital cycles, solar output and volcanoes; each acts on its own time scale.
Long-term global warming is about 1.3–1.4 °C above pre-industrial (1850–1900); Canada has warmed about 1.7 times as fast since 1948 (almost twice as fast since 1970), and the North more than twice as fast.
Indicators: rising temperature and sea level, shrinking Arctic sea ice and glaciers, changing weather extremes, rising CO₂ in the carbon budget.
Correlation is not causation: a causal claim also needs a mechanism and the ruling out of other explanations.

Oceans, Water and Climate Patterns

The oceans have absorbed about 90% of the extra heat trapped by the enhanced greenhouse effect; they are Earth's largest heat sink.
Large bodies of water moderate climate: cooler summers, milder winters and a later, longer fall nearby.
Surface currents are driven by wind; deep (thermohaline) currents by differences in temperature and salinity, which affect density.
Warm currents warm and moisten nearby coasts; cold currents cool and dry them.
Positive feedbacks amplify a change (ice-albedo, water vapour, permafrost); negative feedbacks reduce it (more outgoing infrared from a warmer Earth).
Melting land ice raises sea level; melting floating sea ice barely does.

Ozone Depletion, Ground-Level Ozone and Smog

Ozone (O₃) is good up high (stratospheric ozone absorbs UV) and bad nearby (ground-level ozone is a pollutant in smog).
CFCs release chlorine in the stratosphere, and each chlorine atom can destroy many thousands of ozone molecules because it is regenerated.
The 1987 Montreal Protocol and its later amendments have phased out about 99% of ozone-depleting substances; the ozone layer is projected to recover by about 2040–2066 depending on region.
Ground-level ozone forms when NOₓ and VOCs react in sunlight; smog is ozone plus fine particles.
The ozone hole lets in more UV; the enhanced greenhouse effect traps more infrared. They are different problems.

Impacts of Climate Change and How We Respond

Global impacts include heat waves, drought and desertification, coastal flooding, glacier loss and coral bleaching.
In Canada: shrinking Arctic sea ice (polar bears, Inuit travel and hunting), thawing permafrost, larger wildfires, coastal erosion, and longer but less predictable growing seasons.
Mitigation reduces emissions or increases sinks; adaptation copes with changes that can no longer be avoided.
Canada's stated targets: 40–45% below 2005 emissions by 2030 and net-zero by 2050. The consumer carbon price was set to zero in April 2025; industrial carbon pricing continues.
The IPCC assesses climate science for governments; the Paris Agreement (2015) aims to keep warming well below 2 °C and pursue 1.5 °C.
Judge a claim by its source, purpose, evidence, balance and consistency with other reliable sources.

Unit 4: Light & Geometric Optics

What Light Is: The Electromagnetic Spectrum and Sources of Light

Light is a transverse electromagnetic wave; it needs no medium and travels at $c = 3.00 \times 1 0^{8} m/s$ in a vacuum.
EM spectrum by increasing frequency (and energy): radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.
Visible light runs from about 700 nm (red) to about 400 nm (violet): ROY G BIV.
$c = f λ$ : a shorter wavelength means a higher frequency and more energy.
Light travels in straight lines in a uniform medium, so it can be drawn as rays.
Light sources are named by their energy input: incandescence, electric discharge, fluorescence, phosphorescence, chemiluminescence, bioluminescence, triboluminescence, LED.

Rays, the Laws of Reflection and Plane Mirrors

All angles are measured from the normal, the line perpendicular to the surface.
Law of reflection: $∠ i = ∠ r$ , and the incident ray, reflected ray and normal lie in one plane.
Specular reflection (smooth surface) forms images; diffuse reflection (rough surface) scatters light but still obeys the law at each point.
SALT describes an image: Size, Attitude, Location, Type.
Plane mirror image: same size, upright, same distance behind the mirror, virtual, and laterally inverted.
Real images form where light rays actually meet and can be projected; virtual images form where rays only appear to come from.

Concave and Convex Mirrors with Ray Diagrams

Concave mirrors converge parallel rays to F; convex mirrors diverge them as if from a virtual F behind the mirror.
Focal length is half the radius of curvature: $f = \frac{R}{2}$ .
Concave rays: parallel → through F; through F → parallel; through C → back on itself.
Concave mirror: object beyond C gives a smaller, inverted, real image between C and F; object inside F gives a larger, upright, virtual image behind the mirror; object at F gives no image.
Convex mirror: always smaller, upright, virtual, behind the mirror between V and F.

The Mirror and Magnification Equations

Mirror equation: $\frac{1}{f} = \frac{1}{d _{o}} + \frac{1}{d _{i}}$
Magnification: $M = \frac{h _{i}}{h _{o}} = - \frac{d _{i}}{d _{o}}$
$f$ is positive for concave mirrors and negative for convex mirrors.
$d_{i}$ positive means a real image in front of the mirror; $d_{i}$ negative means a virtual image behind it.
$M$ negative means inverted; $M$ positive means upright. Its size beyond or below 1 tells larger or smaller.

Refraction, Index of Refraction and the Speed of Light

Refraction is the change in direction of light at a boundary, caused by a change in speed.
Index of refraction: $n = \frac{c}{v}$ , with $c = 3.00 \times 1 0^{8} m/s$ ; $n$ has no units and is at least 1.
Into a larger $n$ (slower): bends toward the normal. Into a smaller $n$ (faster): bends away from the normal.
A ray along the normal changes speed but not direction.
Frequency stays the same across a boundary; speed and wavelength change.
Common indices: air 1.00, water 1.33, crown glass 1.52, diamond 2.42.

Snell's Law

Snell's law: $n_{1} sin θ_{1} = n_{2} sin θ_{2}$ , with both angles measured from the normal.
Solve for an angle with $sin θ_{2} = \frac{n _{1} sin θ _{1}}{n _{2}}$ , then take $sin^{- 1}$ .
From air: $n_{2} = \frac{sin θ _{1}}{sin θ _{2}}$ .
$\frac{n _{2}}{n _{1}} = \frac{sin θ _{1}}{sin θ _{2}} = \frac{v _{1}}{v _{2}}$
A ray through a block with parallel faces exits parallel to its original direction, displaced sideways.

Total Internal Reflection, the Critical Angle and Natural Phenomena

Total internal reflection needs light going from larger $n$ to smaller $n$ AND an angle of incidence greater than the critical angle.
Critical angle: $sin θ_{c} = \frac{n _{2}}{n _{1}}$ , where $n_{1} > n_{2}$ ; at $θ_{c}$ the refracted angle is $9 0^{\circ}$ .
Critical angles to air: water $48. 8^{\circ}$ , glass ( $1.50$ ) $41. 8^{\circ}$ , diamond $24. 4^{\circ}$ .
Fibre optics, binocular prisms and diamond sparkle all rely on total internal reflection.
Apparent depth (water, looking straight down) $\approx \frac{real depth}{1.33}$ ; mirages and shimmering come from air layers with different temperatures and indices.

Converging and Diverging Lenses with Ray Diagrams

Converging (convex) lenses are thicker in the middle; diverging (concave) lenses are thinner in the middle.
Converging rays: parallel → through F′; through O → straight; through F → parallel.
Diverging rays: parallel → as if from F (dashed); through O → straight; toward F′ → parallel.
Converging lens: object beyond 2F gives a smaller, inverted, real image (camera); between 2F and F gives a larger, inverted, real image (projector); inside F gives a larger, upright, virtual image (magnifier).
Diverging lens: always smaller, upright, virtual, on the object's side between F and the lens.
Real lens images form on the far side of the lens; virtual ones on the object's side.

The Thin Lens Equation and Magnification

Thin lens equation: $\frac{1}{f} = \frac{1}{d _{o}} + \frac{1}{d _{i}}$
Magnification: $M = \frac{h _{i}}{h _{o}} = - \frac{d _{i}}{d _{o}}$ ; negative $M$ means inverted.
$f$ is positive for converging lenses and negative for diverging lenses.
Positive $d_{i}$ : real image on the far side of the lens. Negative $d_{i}$ : virtual image on the object's side.
For a very distant object, the image forms at the focal point: $d_{i} \approx f$ .

The Eye, Vision Correction and Optical Devices

The eye forms a real, inverted, smaller image on the retina; the cornea does most of the focusing and the lens fine-tunes it.
Accommodation: the eye changes the shape of its lens to focus; a camera moves its lens instead.
Myopia (focus in front of the retina) is corrected with a diverging lens; hyperopia (focus behind) with a converging lens.
Lens power: $P = \frac{1}{f}$ in dioptres with $f$ in metres; negative power means a diverging lens.
Microscope total magnification = objective magnification × eyepiece magnification.
The largest telescopes are reflectors; binoculars use prisms and total internal reflection to make the image upright.