Refraction

Optical Density

Inverse measure of speed of light through transparent medium

Light travels slower in more dense mediaPartial reflection occurs at boundary with

more dense mediumIf 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/vMeasured 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 i) = nr(sin r)

Since nair = 1.00, for light passing from air into another transparent medium,

n = sin i / sin r

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

From Snell’s law: n = sin 90o/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 lensPrincipal focus usually near C; use 2F

instead of C in ray diagramsReal images on opposite side of lens as

object, virtual images on same sideConvex 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 > 2F forms real, reduced image between F and 2F on opposite side

Object at 2F forms real, same size image at 2F on opposite side

Images of Converging Lenses

Object between F and 2F forms real, magnified image beyond 2F 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 sizeOften 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 timesSince 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 imageEyepiece magnifies image of objective

producing greatly magnified, inverted, virtual image

Objective power = tube length/focal lengthTotal magnification M=25length/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