When you face a rainy sky with the sun at your back you see a ring of red light, forming the outer edge of the rainbow, at 42 degrees from the direction of the sunlight, a violet ring at 40 degrees forming its inner edge, and all the other colors of the spectrum in between. The reflected red light is at its greatest intensity at an angle of 42 degrees from the direction of the sun’s rays, while the violet light has maximum intensity at 40 degrees. So when sunlight shines into a sky full of raindrops, it’s encountering millions of tiny, very similar spherical prisms and interacting with each in pretty much the same way: each produces a basically identical pattern of refracted, dispersed, reflected, and re-refracted light in a spectrum of colors. Light rays emitted by the sun are effectively parallel when they reach the earth, and raindrops are effectively all the same shape. When the reflected light exits the drop and re-enters the air, it’s refracted and dispersed a second time. The ratio of light transmitted to light reflected is, once again, a function of the angle at which the ray hits the surface.Ĥ. ![]() Most of the light striking the raindrop passes straight through it and out the far side, but some of it reflects off the rear interior surface of the drop and is sent in some new direction. Meanwhile, the drop is acting as a prism, splitting the white light of the ray into its component colors by refracting the different wavelengths at different angles: red wavelengths bend a certain amount, orange wavelengths a slightly different amount, and so on.ģ. The angle of the bend is determined by (a) the intrinsic light-transmitting properties of air and water (every transparent substance has its own individual index of refraction) and (b) the angle at which the ray strikes the surface of the spherical droplet - whether, e.g., it hits the drop squarely or strikes a glancing blow off to one side.Ģ. When a ray of sunlight strikes a raindrop, the ray refracts, or bends, at the point where it passes out of the air and into the water of the drop. How do these occur? Why did the second faint rainbow (which was on top of the first) have the opposite color sequence? nyountĪh, rainbows - those will-o’-the-wisps of ethereal beauty, made possible only by a full lineup of optics phenomena. cotk d.Dear Straight Dope: While on vacation recently our family saw a double rainbow. If tan x = >, what is cos 2x, given that 0 < kiai. If a sample has 120 grams of radioactive material, what equation could be used to determine the amount of material remaining (v) after x years. A certain radioactive isotope has a half life of 5 years. reflection about the x-axis, vertical translation 5 units down, vertical compression by a factor of 2. vertical translation 5 units down, vertical compression by a factor of, reflection about the x-axis. reflection about the y-axis, vertical stretch by a factor of 2, vertical translation 5 units up. reflection about the x-axis, vertical compression by a factor of, vertical translation 5 units down. State the transformations, in proper order, that are needed to turn f(x)=-8 logoX+6 into f(x)=4 logo-x+1. ![]() For which of the following expressions would it NOT be useful to employ a double angle formula in order to calculate? 2 tan 15° a. What double angle formula can be appropriately used to derive algebraically a formula for sin a.
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