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.
Thin Lens Equation
Thin lens equation: 1/f = 1/do + 1/di. Magnification = -di/do. Negative m = inverted image.
Thin Lens Equation
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.