Proven Mnemonics & Acronyms — fast to learn, hard to forget.
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Law of Reflection
Angle of incidence = angle of reflection
Law of Reflection
Light bounces off a mirror at the same angle it arrived
Both angles measured from the normal (perpendicular to the surface). Flat mirror: angle in = angle out. This is how billiard ball bounces are predicted.
Refraction
Snell's Law: n₁sinθ₁ = n₂sinθ₂
Refraction
Light bends when crossing between materials of different optical density
n = refractive index. Higher n = slower light = more bending. Light going from air to glass bends toward the normal. From glass to air it bends away.
Lens Types
Convex = converging, Concave = diverging — conCAVE is caved in
Lens Types
Convex lenses focus light; concave lenses spread it
Convex (thicker in middle): magnifying glasses, cameras, eyes. Concave (thinner in middle): corrects nearsightedness, flashlights. Memory trick: conCAVE is caved in at the middle.
Total Internal Reflection
Total internal reflection: light trapped inside a denser medium — basis of fiber optics
Total Internal Reflection
When light can't escape a denser medium — used in fiber optic cables
When light hits a boundary at an angle greater than the critical angle, it reflects entirely back inside. No refraction out. Critical angle = arcsin(n₂/n₁). Fiber optics, diamonds, and mirages all use this.
Locating images formed by converging and diverging lenses
f = focal length (positive for converging, negative for diverging). do = object distance. di = image distance (positive = real image on other side; negative = virtual image on same side as object). Magnification m = -di/do. |m| > 1 = enlarged. |m| < 1 = reduced.
Mirror Equation
Mirror equation: 1/f = 1/do + 1/di. Concave mirror: f positive (converging). Convex: f negative (diverging).
Mirror Equation
Locating images formed by curved mirrors
Same equation as thin lens but for mirrors. Concave (converging) mirror: f is positive. Used in telescopes, flashlights, makeup mirrors. Convex (diverging) mirror: f is negative. Always produces virtual, upright, reduced images. Used in car side mirrors and security mirrors — wider field of view.
Dispersion of Light
Dispersion: white light splits into spectrum in a prism. Violet bends most (highest n). Red bends least.
Dispersion of Light
Why a prism separates white light into a rainbow
Different wavelengths of light travel at slightly different speeds in glass — different refractive indices. Violet light has the highest refractive index → bends most. Red light has the lowest → bends least. Rainbows are caused by dispersion and internal reflection inside water droplets.
Index of Refraction
Index of refraction: n = c/v. Higher n = slower light = more bending. Diamond n=2.42, water n=1.33.
Index of Refraction
How much a material slows light down
n = c/v where c = speed of light in vacuum, v = speed of light in medium. n is always ≥ 1. Higher n: light travels more slowly and bends more when entering from air. Vacuum: n=1.000. Air: n=1.0003. Water: n=1.33. Glass: n~1.5. Diamond: n=2.42.
Diffraction Gratings
Diffraction grating: multiple slits → sharp bright spots. d sinθ = mλ for constructive interference.
Diffraction Gratings
Many slits create sharper, more widely separated interference maxima
Grating equation: d sinθ = mλ (m = order number: 0, ±1, ±2...). d = slit spacing. More slits → sharper, brighter maxima. Used in spectrometers to measure wavelengths of light. CDs and DVDs work as reflection diffraction gratings — different wavelengths reflect at different angles → rainbow colors.
Fiber Optic Principles
Fiber optics: total internal reflection keeps light trapped inside the fiber. Critical angle = arcsin(n₂/n₁).
Fiber Optic Principles
How light travels through optical fibers without escaping
Light enters fiber at a shallow angle → hits the boundary at angle greater than critical angle → total internal reflection → light bounces along the fiber. Core has higher refractive index than cladding. Single-mode fiber: one light path, used in telecommunications. Multi-mode: multiple paths, shorter distances.
The Human Eye as an Optical System
Human eye: cornea and lens form real, inverted image on retina. Nearsighted: image in front of retina (concave lens). Farsighted: behind retina (convex lens).
The Human Eye as an Optical System
How vision works — and how lenses correct it
The eye is a converging optical system. Cornea does most focusing; lens fine-tunes. Image formed on retina is real and inverted — brain flips it. Nearsighted (myopia): eyeball too long or lens too strong → image forms in front of retina → corrected by diverging (concave) lens. Farsighted: opposite — corrected by converging (convex) lens.
Double-slit interference — when waves add up or cancel out
Two coherent sources create a stable interference pattern — bright and dark bands
Constructive interference: path difference = mλ (m = 0, 1, 2...) — bright fringes. Destructive interference: path difference = (m + ½)λ — dark fringes. Double-slit fringe spacing: y = mλL/d where L = screen distance, d = slit separation. Thin film interference: accounts for phase shift on reflection (light going from low to high n flips phase by π — like reflection off fixed end). Newton's rings: circular interference pattern from spherical lens on flat glass.
Constructive
Path diff = mλ — waves in phase, amplitudes add
Destructive
Path diff = (m+½)λ — waves out of phase, cancel
Thin film
Phase shift on reflection from denser medium — adds half wavelength
Polarization of Light
Malus's Law: I = I₀cos²θ — intensity depends on angle between polarizer and analyzer
How polarizers filter light and Malus's Law for transmitted intensity
Unpolarized light through a polarizer loses half its intensity — then Malus's Law applies
Unpolarized light: electric field oscillates in all transverse directions. Linear polarizer: passes only one plane of oscillation. Unpolarized → polarizer: intensity halved (I = I₀/2). Polarizer → analyzer at angle θ: I = I₀cos²θ (Malus's Law). At θ = 90° (crossed polarizers): I = 0 — no light passes. Brewster's angle: angle of incidence where reflected light is completely polarized: tan(θ_B) = n₂/n₁. Applications: sunglasses (reduce glare), LCD screens, 3D movies, photography.
Malus's Law
I = I₀cos²θ — angle between polarizer and analyzer
Crossed at 90°
No light passes — complete extinction
Brewster's angle
Reflected light fully polarized — tan θ_B = n₂/n₁
Microscopes and Telescopes
Microscope: two converging lenses magnify small. Telescope: two lenses bring distant close.
How compound microscopes and refracting telescopes use two lenses
Both instruments use an objective lens and an eyepiece — but for opposite purposes
Compound microscope: objective (short focal length) forms enlarged real image of nearby object. Eyepiece acts as magnifying glass — views that image. Total magnification = m_obj × m_eye. Resolution limit: d_min = 0.61λ/NA where NA = n sin θ. Refracting telescope: objective (long focal length) forms real image of distant object at its focal plane. Eyepiece magnifies that image. Angular magnification = f_obj / f_eye. Large f_obj → higher magnification. Reflecting telescope (Newton): uses concave mirror instead of objective lens — avoids chromatic aberration.
Microscope mag
m_obj × m_eye — both lenses multiply magnification
Telescope mag
f_obj / f_eye — longer objective = more power
Reflecting
Mirror instead of lens — no chromatic aberration
Chromatic Aberration and Aberrations
SCCA — Spherical, Chromatic, Coma, Astigmatism — four lens aberrations
Four types of optical aberrations that blur or distort images in real lenses
Real lenses are imperfect — aberrations are why camera lenses have multiple elements
Chromatic aberration: different wavelengths (colors) refract at different angles → lens focuses red and blue at different points → color fringing. Fixed by achromatic doublet (two lenses of different glass). Spherical aberration: rays hitting edge of lens focus at different point than rays through center → blurry image. Fixed by aspherical lens or stop. Coma: off-axis point sources appear comet-shaped. Astigmatism: different focal lengths in vertical vs horizontal planes. Modern cameras use 7-10+ lens elements to minimize all aberrations.
Chromatic
Different colors focus at different distances — color fringing
Spherical
Edge vs center rays focus differently — blurry spots
Fix
Achromatic doublet for chromatic, aspherical for spherical
🎓 Common Exam Questions
Q: Explain refraction and derive Snell's Law from Fermat's Principle.
A: Refraction: when light passes from one medium to another, it changes speed and bends. Index of refraction: n = c/v where v is the speed of light in the medium. Snell's Law: n₁sinθ₁ = n₂sinθ₂ where angles are measured from the normal. When light goes from low n to high n (e.g., air to glass), it bends toward the normal. From high n to low n, it bends away. Fermat's Principle: light takes the path that minimizes travel time — Snell's Law is the mathematical consequence. Total internal reflection: when going from high n to low n at angle greater than critical angle θ_c = arcsin(n₂/n₁). Applications: fiber optics, diamond brilliance (high n = 2.42), mirages (temperature gradient bends light), corrective lenses.
Q: Explain how converging and diverging lenses form images using the thin lens equation.
A: Thin lens equation: 1/f = 1/d_o + 1/d_i. Magnification: m = −d_i/d_o = h_i/h_o. Sign convention: distances positive if on the correct side (real = positive). Converging lens (f positive): object beyond 2f → real, inverted, smaller image. Object between f and 2f → real, inverted, larger image. Object inside f → virtual, upright, larger image (magnifying glass). Diverging lens (f negative): always produces virtual, upright, smaller image regardless of object position. Power of a lens: P = 1/f (in diopters when f in meters). Corrective lenses: nearsighted (myopia) — image forms in front of retina, needs diverging lens. Farsighted (hyperopia) — image forms behind retina, needs converging lens.
Q: Explain Young's double-slit experiment and what it proved about the nature of light.
A: Young's double-slit experiment (1801): light passes through two narrow slits and creates an interference pattern of bright and dark bands on a screen. Bright fringes (constructive): path difference = mλ where m = 0, ±1, ±2... Position of bright fringes: y_m = mλL/d where L = distance to screen, d = slit separation. Dark fringes (destructive): path difference = (m + ½)λ. This experiment conclusively proved that light behaves as a wave — only waves can interfere. Newton's corpuscle theory could not explain the interference pattern. Later, the photoelectric effect showed light also behaves as particles — establishing wave-particle duality. The experiment works with single photons (or electrons) sent one at a time — interference is a quantum phenomenon of probability amplitudes.
Q: What are the mirror equation and sign conventions for concave and convex mirrors?
A: Mirror equation: 1/f = 1/d_o + 1/d_i. For mirrors, f = R/2 where R is the radius of curvature. Sign convention: distances are positive in front of the mirror (real), negative behind (virtual). Concave mirror (f positive): object beyond C (center of curvature) → real, inverted, smaller image. Object between f and C → real, inverted, larger image. Object inside f → virtual, upright, larger image (like a makeup mirror). Convex mirror (f negative): always produces virtual, upright, smaller image with wider field of view — used for security mirrors and car side mirrors ('objects are closer than they appear'). Magnification: m = −d_i/d_o. Concave mirrors focus parallel rays to the focal point — used in telescopes (Newtonian), satellite dishes, and solar concentrators.
Q: Explain polarization of light and Malus's Law.
A: Unpolarized light has electric field oscillating in all transverse directions. A linear polarizer transmits only the component along its transmission axis. Unpolarized light through a polarizer: intensity halved, I = I₀/2. Polarized light through a second polarizer (analyzer) at angle θ: Malus's Law I = I₀cos²θ. At θ = 90° (crossed polarizers): I = 0. Brewster's angle: incident angle where reflected light is completely polarized — tan(θ_B) = n₂/n₁. At Brewster's angle, reflected and refracted rays are perpendicular. Applications: polarized sunglasses block horizontally polarized glare from flat surfaces; LCD screens use crossed polarizers with liquid crystals to control light transmission; 3D cinema uses polarized light (different polarizations for each eye); stress analysis in engineering (photoelasticity).