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Exploring Optical Refraction in Transparent Media

Understand the physics of refraction through different media, from Snell's Law to total internal reflection, including dispersion and lens terms. Learn about mirages, rainbows, and lens equations.

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Exploring Optical Refraction in Transparent Media

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  1. Refraction

  2. 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

  3. 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

  4. 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

  5. Snell’s Law • Relates index of refraction to the angle of refraction • Between any two media ni(sin qi) = nr(sin qr) • Since nair = 1.00, for light passing from air into another transparent medium, n = sin qi/ sin qr

  6. 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

  7. Mirage Formation

  8. Highway Mirage

  9. 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

  10. 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

  11. 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

  12. Dispersion in Raindrops

  13. Rainbow Physics

  14. 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

  15. Total Reflection • From Snell’s law: n = sin 90o/sin icso 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

  16. Total Internal Reflection

  17. Fiber Optics

  18. 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

  19. 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

  20. 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

  21. 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

  22. 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

  23. 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)

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

  25. 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)

  26. 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

  27. 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/fe fo( all in cm)

  28. 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

  29. 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

  30. 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

  31. 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

  32. 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

  33. 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

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