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°, 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
• Snell's Law: index of refraction equals ratio of sine of incident angle divided by sine of refracted angle - n = sin i/ sin r
• Measured by refractometer, used to test purity of substance

Atmospheric Refraction

• Causes gradual curve of light from stars and sun
• Makes sun visible 2-3 min. before sunrise and after sunset

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

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°
• At critical angle, refracted ray parallel to media boundary
• From Snell's law: n = sin 90°/sin i_c so sin i_c = 1/n
• Critical angle for water is 48.5°, for diamond it is 24°
• If incident angle > critical angle, total reflection occurs
• Causes diamond's sparkle, 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
• Virtual focus (diverging or converging) where light rays appear to have originated
• Virtual imageforms 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
• 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 (case 4)
• Eyepiece magnifies image of objective (case 6)
• Objective power = tube length/focal length
• Total magnification M=25length/f_e f_o ( all in cm)

The Telescope

• Refracting telescopes have large objective lens for max. light
• Object at great distance means small, real image
• Eyepiece lens enlarges objective image
• Binoculars, terrestrial telescopes use extra lens or prism to invert image to upright

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
• 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
• Everybody sees their own rainbow

Color

• Determined by frequency of light
• Hot bodies produce different frequencies of light depending on temp. - red hot, white hot
• Color of object depends on light frequencies reflected (or not absorbed)
• Color of transparent object depends on light transmitted (or not absorbed)

Complimentary Colors

• Primary colors of light are red, blue, green
• When combined, produce white (polychromatic) light
• If one color is removed from white light, complimentary color results
• Mixing light is additive process - color TV, stage lighting
• Complimentary color pairs
  • Red and cyan (blue-green)
  • Blue and yellow
  • Green and magenta (red-blue)
• Any color can be produced from a combination of red, blue, and green lights

Subtractive Mixing

• Mixing of pigments is subtractive process
• Pigment absorbs certain frequencies, reflecting color we see
• Primary pigments are cyan, magenta, yellow
• Used in paints, color printing, color photography

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