ROYGBIV: Red Orange Yellow Green Blue Indigo Violet
Visible Spectrum
Colors of visible light in order from lowest to highest frequency
Red has lowest frequency (longest wavelength). Violet has highest (shortest). Red bends least in a prism; violet bends most. Remember: Richard Of York Gave Battle In Vain.
R
Red β lowest frequency
O
Orange
Y
Yellow
G
Green
B
Blue
I
Indigo
V
Violet β highest frequency
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: nβsinΞΈβ = nβsinΞΈβ
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 β 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 β basis of fiber optics
Total Internal Reflection
When light can't escape a denser medium β 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(nβ/nβ). 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 β 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 β different refractive indices. Violet light has the highest refractive index β bends most. Red light has the lowest β 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 β₯ 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 β sharp bright spots. d sinΞΈ = mΞ» for constructive interference.
Diffraction Gratings
Many slits create sharper, more widely separated interference maxima
Grating equation: d sinΞΈ = mΞ» (m = order number: 0, Β±1, Β±2...). d = slit spacing. More slits β sharper, brighter maxima. Used in spectrometers to measure wavelengths of light. CDs and DVDs work as reflection diffraction gratings β different wavelengths reflect at different angles β rainbow colors.
Fiber Optic Principles
Fiber optics: total internal reflection keeps light trapped inside the fiber. Critical angle = arcsin(nβ/nβ).
Fiber Optic Principles
How light travels through optical fibers without escaping
Light enters fiber at a shallow angle β hits the boundary at angle greater than critical angle β total internal reflection β 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 β 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 β brain flips it. Nearsighted (myopia): eyeball too long or lens too strong β image forms in front of retina β corrected by diverging (concave) lens. Farsighted: opposite β corrected by converging (convex) lens.