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1 Lecture Notes (Refraction of Light) Intro: - the bending of light that occurs at a boundary of a transparent object is called refraction - the angle of incidence and the angle of refraction is measured with respect to the normal to the surfacee - when light hits the boundary at an angle of zero degrees, there is no refraction n, therefore light does not bend

2 - as the angle of incidence increases, the amountt of bending increases (the angle of refraction differss more and more from the angle of incidence) Index of Refraction: - the overall amount of bending that occurs when light enters a material depends of the incident angle and the index of refraction - the index of refraction is an optical property of the material

3 - a mathematical rule, called Snell's Law, will calculate the refracted angle if you know the angle off incidence and the index of refraction sin θ - the equation for the index of refraction is: n i sin θ ; where n is r the symbol for index of refraction, θ i is the angle of incidence, and θ r is the angle of refraction - a more general case of this is expressed as: ni sin θi n r sin θ r - the index of refraction is a measure off how much light bends when it passes into a medium from a vacuum - if no bending takes place then the material has refraction very close to 1 and index of - as bending increases, so does the index of refraction; for example, water (n = 1.33) causes light to bend more than air (n = ), and diamondd (n = 2.42) causess light to bend the most

4 Basic Rules of Refraction: - the bending is ultimately caused by a change in speed of light - remember, when light bends as it passes from air to glass, water, or other materials where light travels more slowly, it is bent toward the normal - the beam in the first mediumm is called the incident ray, and the beam in the second medium is called the refracted ray - in the situation of light traveling from higher speed to a lower speed medium, the angle of incidence will be greater than that of the angle of refraction - you can state this algebraically as: θ r < θ i - when light is refracted and θr < θ i, then the second medium is said to be more optically densee than the first medium - conversely, if light is moving from a more optically dense to a lesser one and θ r > θ i, then light will bend away from the normal - if light strikes a surface along the perpendicular, θ i and zero and the light wave does not changee direction θ r are

5 Total Internal Reflection: - there are times when light cannot passs between two substances, even if they are both transparen nt - this situation arises when you have light traveling at large incident angles from a mediumm of greater opticall density (greater index of refraction) to a medium of lesser opticall density - at a particular angle, called the critical angle, the refracted light ray reaches 90 - beyond the critical angle, light no longer leaves the material

6 Applications of Total Internal Reflection: - one application of total internal reflection is the use of solid glass or transparent plastic rods that are only as thick as a human hair to "pipe" light from one place to another; this is called fiber optics - light is confined to traveling within the rods even around curves as a result of successive internal reflections; also very little light intensity is lost even over vast distancess - fiber optics have revolutionized the communications industry; they have allowed high volumes of internet traffic, radio/television signals, and telephone e calls to be carried over very long distances with very small cables - fiber optics are used in medicine to detect and ailments such as colon cancer diagnose certain - in a procedure called endoscopy, doctors examine the lining of your colon (large intestine) for abnormalities by inserting a flexible fiber optic cable as thick as your finger into your anus and slowly advancing it into the rectum and colon

7 Atmospheric Refraction: - on Earth, we live under a vast amountt of air; itt is called the atmosphere - the atmosphere is not uniform, and it temperature varies in density and - the atmospheric index of refraction depends on the density of the air; thereforee the index of refraction decreases as you go higher into the sky - the result is that objects in the sky appear in places that their true positions are not

8 - this causes sunlight, in the morning, to reach us before the sun is actually on the horizon - conversely, this process allows us to see sunlight at dusk even though the sun has actually already set Mirages: - this phenomenon of light changing speeds is responsible for mirages - in mirages, wavefronts coming from the top of objects will bend as they approach the ground; this is duee to the fact that the air is warmer and less densee near the ground

9 - the light will bend upward, allowing the observer to see an object as he/she looks downward the top of Looming: - objects may appear to be floating in air; this effect is known as looming - looming occurs when the surface is very cold, water such as over cold

10 - the cold surface will cause the atmospheric density to decrease and have the make light rays bend downward Dispersion: - dispersion is the process by which white light splits up into the spectrum of colors - a spectrum is produced because each color refracts differently; blue light bends thee most and red light the least - dispersion also produces rainbows; a rainbow is often seen by an observer positioned between the Sun and a rain shower

11 Rainbows: - the individual rain drops act like small prisms sunlight which refract - if a raindrop high in the sky is being observed,, the observer will see red light because it bends the most; a lower raindrop will be seen orange, yellow, etc... until you finally see violet light which bends the least Halos: - atmospheric halos are sometimes seen around the Sun or Moon - these effects are cause by atmosphericc ice crystals refracting sunlight

12 - halos are generated by hexagonal ice crystals which concentrates light at 22

13 - other effects can be generated by ice crystals, such as sundogs - sundogs create "ghost" suns within the halo on each side of the Sun at the same height of the Sun Cameras: - cameras are devices which use lenses photographic film to capture images on - cameras typically have adjustable lenses whichh allow you to focus an image onto the film - even when you focus the image to thee best of your ability, there willl be regions where light reflecting from the image willl not meet at the focus - lenses have aberrations which will cause light to not meet at the focus; two common types are chromatic c and spherical aberrations

14 Chromatic Aberratio on: - this occurs when different wavelengths of light refracted by a lens focus at different points - when white light which is composed of many colors passes through a lens, blue light rays are refracted more than red light rays for a convex lens; therefore the focal length of blue light is less than that of red light - the opposite holds true for concave lenses - here is an picture that sufferss from chromatic aberration

15 - this effect can be corrected by using a combination of converging and diverging lenses made from different type of glasss Spherical Aberration: - most photographic lenses are composed of elements with spherical surfaces; such elements are relatively easy to manufacture, but their shape is not ideall for the formation of a sharp image - this problem resultss from the fact thatt the focall point of light rays far from the principal axis of a sphericall lens or mirror are from the focal point of rays passing near the principal axis - in this diagram, rays near the middle of the lens are imaged farther from the lens than rays at the edges; this results in no single focal length for the lens - cameras use an adjustable aperture to reduce spherical aberration; as the aperture is reduced, sharper images are producedd because only the central portion of the lens is exposed to the incident light

16 Eyes: - images are formed as light passes through the lens of our eye and strikes the retina - the images formed on the retina are inverted, but our brains will interpret them as right-side up - the ability of the eyee to focus decliness as we age because the elasticity of our lens will decrease over time - as a result, corrective lenses are used for our eyes to porperly focus images - myopia (nearsightedness) occurs when the eyee is too long, and images focus before hitting the retina

17 - individuals with myopia (nearsightedness) can see things close up, but have trouble seeing things far away - hyperopia (farsightedness) occurs when the eye is too short, and images focus beyond the retina - people with hyperopia (farsightedness) can seee things far away, but have trouble seeing things close up

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