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 n i (sin  i ) = n r (sin  r )  Since n air = 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 90 o /sin i c so sin i c = 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 2F 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 > 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 size  Often used to neutralize or minimize effect of converging lens (glasses)

Lens Equations  1/f = 1/d o + 1/d i  h i / h o = d i / d o  For simple magnifier, magnification M = h i / h o = d i / d o for normal vision, d i = 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=25length/f e f o ( 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