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A triangular prism has an apex angle of 45 degrees.
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The minimum angle of deviation of the prism is 55 degrees.
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What is the angle of incidence that corresponds to this angle of deviation?
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Answer to the nearest degree.
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Here, weโre working with a prism, where the apex angle ๐ด is equal to 45 degrees.
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Along with this, weโre told that when a ray of light passes through the prism, the smallest angle that this ray can be deviated โ thatโs this angle here โ is equal to 55 degrees.
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And weโll call this smallest angle ๐ผ zero.
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Knowing all this, we want to solve for the angle of incidence of this ray.
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That angle is shown here, and weโve called it ๐ zero.
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To solve for ๐ zero, we can recall a mathematical relationship between these three variables highlighted.
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Whenever a light ray passes through a prism with apex angle ๐ด, if that ray is deviated at the minimum possible angle โ weโve called that angle ๐ผ zero โ then the angle of incidence ๐ zero of this ray equals ๐ผ zero plus ๐ด all divided by two.
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In our case, since weโre given values for ๐ผ zero and ๐ด, we can substitute those in and then solve for ๐ zero.
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๐ผ zero, we know, is 55 degrees.
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๐ด is 45 degrees.
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55 plus 45 is 100 so that overall ๐ zero is 50 degrees.
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To the nearest degree, this is the angle of incidence corresponding to the minimum angle of deviation for this prism.