Refraction Optical Density Inverse measure of speed of

Refraction

Optical Density ¬Inverse measure of speed of light through transparent medium ¬Light travels slower in more dense media ¬Partial reflection occurs at boundary with more dense medium ¬If incident angle not 90 degrees, refraction occurs

Optical Refraction ¬Bending of light rays as they pass obliquely from one medium to another of different optical density ¬Angle of refraction measured to normal from refracted ray ¬Passing from lower to higher density, light refracted towards normal; high to low, away from normal

Index of Refraction ¬Ratio of speed of light in a vacuum (c) to its speed in a substance ¬n =c/v ¬Measured by refractometer, used to test purity of substance

Snell’s Law ¬Relates index of refraction to the angle of refraction ¬Between any two media ni(sin qi) = nr(sin q r) ¬Since nair = 1. 00, for light passing from air into another transparent medium, n = sin qi / sin qr

Atmospheric Refraction ¬Causes gradual curve of light from stars and sun ¬Creates mirages that look like wet spots on roads ¬Makes sun visible 2 -3 min. before sunrise and after sunset

Mirage Formation

Highway Mirage

Laws of Refraction ¬Incident ray, refracted ray & normal line all lie in same plane ¬Index of refraction for homogeneous medium is constant, independent of incident angle ¬Oblique ray passing from low to high optical density is bent towards normal and vice versa

Dispersion ¬Transparent media react differently to different wavelengths, slowing short waves more than long waves ¬Different wavelengths are refracted to a different degree, violet more than red ¬Causes spreading of the light according to wavelength (frequency) - rainbow

Dispersion ¬Prisms, water drops readily disperse light due to non-parallel surfaces ¬Rainbows created by refraction through many drops ¬Each color produced by a set of drops at a certain angle from the eye

Dispersion in Raindrops

Rainbow Physics

Total Reflection ¬At media boundary, light from denser medium refracted back into it, rather than exiting into less dense medium ¬Critical angle: incident angle that produces refracted angle of 90 degrees ¬At critical angle, refracted ray parallel to media boundary

Total Reflection o ¬From Snell’s law: n = sin 90 /sin ic so sin ic = 1/n ¬Critical angle for water is 48. 5 deg. , for diamond it is 24 deg. ¬If incident angle > critical angle, total reflection occurs ¬Causes diamond’s sparkle, fiber optics

Total Internal Reflection

Fiber Optics

Lenses ¬Transparent object with nonparallel surfaces, at least one of which is curved ¬Usually glass or plastic but can be water, air, other transparent solid, liquid or gas ¬Converging: thicker in middle, converges (focuses) rays ¬Diverging: thinner in middle, diverges (spreads) rays

Lens Terms ¬Each side of lens has center of curvature and focus ¬Real focus (converging lens) where light rays pass through ¬Real image forms on same side of lens as real focus, opposite side of object

Lens Terms ¬Virtual focus (diverging or converging) where light rays appear to have originated ¬Virtual image forms on same side of lens as virtual focus and object ¬Focal length: distance from center of lens to focal point; depends on curvature and index of refraction of lens

Mirrors & Lenses: Differences ¬Secondary axes pass through center of lens ¬Principal focus usually near C; use 2 F instead of C in ray diagrams ¬Real images on opposite side of lens as object, virtual images on same side ¬Convex lenses are like concave mirrors, concave lenses like convex mirrors

Images of Converging Lenses ¬Object at infinite distance forms point image at F on opposite side ¬Object at finite distance > 2 F forms real, reduced image between F and 2 F on opposite side ¬Object at 2 F forms real, same size image at 2 F on opposite side

Images of Converging Lenses ¬Object between F and 2 F forms real, magnified image beyond 2 F on opposite side ¬Object at F forms no image, rays are parallel ¬Object between F and lens forms enlarged, virtual image on same side (magnifying glass)

Images of Diverging Lenses ¬Always virtual, erect, reduced size ¬Often used to neutralize or minimize effect of converging lens (glasses)

Lens Equations ¬ 1/f = 1/do + 1/di ¬hi / ho = di / do ¬For simple magnifier, magnification M = hi / ho = di / do for normal vision, di = 25 cm, so M = 25 cm/f (f - focal length)

f-numbers ¬Ratio of focal length to aperture (effective diameter), used to rate camera lenses ¬Determines light gathering power of lens ¬“Fast” lenses have low f-numbers, gather more light, need shorter exposure times ¬Since area of lens is prop. to square of diameter, f-2 lens is 4 times faster than f-4, 16 times faster than f-8

The Microscope ¬Objective lens forms enlarged, real image ¬Eyepiece magnifies image of objective producing greatly magnified, inverted, virtual image ¬Objective power = tube length/focal length ¬Total magnification M=25 length/fe fo ( all in cm)

Telescopes ¬Reflectors have one converging mirror and a converging eyepiece lens ¬Refracting telescopes have large objective lens instead of a mirror ¬Object at great distance means small, real image is produced by objective mirror or lens

Telescopes ¬Eyepiece lens enlarges objective image producing magnified, inverted, virtual image ¬Large telescopes are reflectors due to size and expense of large lens ¬Binoculars, terrestrial telescopes use extra lens or prism to invert image to upright position

The Eye ¬Cornea and lens work together to focus light on retina producing inverted, small image ¬Brain circuitry inverts image so it seems right side up

Vision Correction ¬Nearsighted means light focuses in front of retina—corrected with diverging lens ¬Farsighted means light would focus behind retina—corrected with converging lens

Cameras ¬Cameras focus light on the focal plane where the film is located ¬Produce real, inverted, smaller image, like the eye ¬Some cameras use a diverging lens for a viewfinder

Lens Aberrations ¬Spherical aberration: like mirrors, light passing through edges not focused at same point as through center - correct with lens combination ¬Chromatic aberration: different colors refracted differently, focus at different points - correct with lens coatings, lenses of different materials