If the angle of deviation due to refraction of an equilateral prism is 40°, what is the angle of incidence with the prism if the path of the ray through the prism is parallel to the plane of the prism?
Question
If the angle of deviation due to refraction of an equilateral prism is 40°, what is the angle of incidence with the prism if the path of the ray through the prism is parallel to the plane of the prism?
Solution
To solve this problem, we need to use the formula for the angle of deviation in a prism, which is given by:
δ = i + e - A
where: δ is the angle of deviation, i is the angle of incidence, e is the angle of emergence, and A is the angle of the prism.
Given that the prism is equilateral, the angle of the prism A is 60°. The path of the ray through the prism is parallel to the base, which means the angle of emergence e is equal to the angle of incidence i.
So, we can rewrite the formula as:
δ = 2i - A
We know that δ is 40° and A is 60°. Substituting these values into the formula, we get:
40° = 2i - 60°
Solving for i, we get:
2i = 40° + 60° = 100°
Therefore, the angle of incidence i is 100°/2 = 50°.
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