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The expression for the angle of deviation

Answer to Problem 18P
The expression for the angle of deviation is
Explanation of Solution
The schematic ray diagram involving the prism is shown in Figure 1. The refractive index of the medium outside the prism is
From the Figure 1, the following relations can be deduced.
Solve equation (I) for
Use equation (III) in (II).
Apply Snell’s law to the boundary where light enters the prism.
Solve equation (V) for
Use equation (IV) in (VI).
Use the approximation
Use the approximation
Use
In the triangle formed by the ray crossing the prism and the two surfaces of the prism, the angles are
Solve equation (XI) for
Use equation (X) in (XII).
Apply Snell’s law to the boundary where light leaves the prism.
Use
Use equation (XIII) in (XV).
Since
Write the expression for the angle of deviation
Use equation (XVII) and (IV) in (XVIII).
This indicates that, the angle of deviation
Conclusion:
Therefore, the expression for the angle of deviation is
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