Refraction & Prisms: Angle of Incidence Explained

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The discussion centers on the relationship between the angle of incidence and the angle of refraction in a prism, specifically noting that their sum equals 60 degrees. This is explained through the geometry of a triangle formed by the light ray and the prism's borders, where the sum of the interior angles is always 180 degrees. One angle in this triangle is established as 60 degrees, while the other two angles are defined as 90 degrees minus the angle of incidence (i) and 90 degrees minus the angle of refraction (r). The conversation emphasizes the importance of understanding the geometric principles at play in refraction. Overall, the geometric relationships help clarify the behavior of light as it passes through a prism.
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That is a page from my textbook. The book mentions that the angle of incidence on the right side when added with the angle of the refraction equals 60 degrees. Why is that?
 
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Consider the triangle formed by the light ray in the prism and the two prism borders. The sum of the interior angles is 180°, and one angle is 60°. Everything else follows from geometry with the right angles there.
 
Which triangle? If you mean the one formed by the refracted ray, it is not a right angle triangle.
 
Triangle ABC:
$$
\angle A + \angle B + \angle C = 180^0
$$
Or triangle formed by B, C, and the prism's apex.
 

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Another way to look at it. The very top triangle has one angle of 60°. The other two angles are 90- i and 90-r etc. etc...
 
sophiecentaur said:
Another way to look at it. The very top triangle has one angle of 60°. The other two angles are 90- i and 90-r etc. etc...
That is the triangle I meant.
And the sum of those three angles is 180 degrees.
 
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