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(B) The deviation formula for a prism is given by $\delta = i + e - A$,where $i$ is the angle of incidence,$e$ is the angle of emergence,and $A$ is th

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$49$

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(B) The deviation formula for a prism is given by $\delta = i + e - A$,where $i$ is the angle of incidence,$e$ is the angle of emergence,and $A$ is the prism angle.Given that the deviation $\delta = 44^\circ$ for $i = 42^\circ$ and $i = 62^\circ$,we know that for a prism,if the deviation is the same for two different angles of incidence,then $e_1 = i_2$ and $e_2 = i_1$.Thus,$44^\circ = 42^\circ + 62^\circ - A$.$44^\circ = 104^\circ - A \Rightarrow A = 60^\circ$.For minimum deviation,the condition is $i = e$,and the formula is $\delta_{min} = 2i - A$.Substituting the given values: $38^\circ = 2i - 60^\circ$.$2i = 98^\circ \Rightarrow i = 49^\circ$.

$A$ certain prism is found to produce a minimum deviation of $38^\circ$. It produces a deviation of $44^\circ$ when the angle of incidence is either $42^\circ$ or $62^\circ$. What is the angle of incidence when it is undergoing minimum deviation (in $^\circ$)?

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