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(C) For a prism,the angle of deviation $\delta = i + e - A$. The deviation $\delta$ is a function of the angle of incidence $i$. The graph of $\delta$

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(C) For a prism,the angle of deviation $\delta = i + e - A$. The deviation $\delta$ is a function of the angle of incidence $i$. The graph of $\delta$ versus $i$ is a parabola-like curve that is symmetric about the angle of minimum deviation $\delta_{min}$.In the given case,for $i_1 = 53^{\circ}$,the angle of emergence is $e_1 = 37^{\circ}$.Since the prism formula is symmetric with respect to $i$ and $e$ (i.e.,if $i$ and $e$ are interchanged,the deviation remains the same),the angle of minimum deviation occurs at $i = e = \frac{53^{\circ} + 37^{\circ}}{2} = 45^{\circ}$.When $i = 53^{\circ}$,$e = 37^{\circ}$.When $i = 37^{\circ}$,$e = 53^{\circ}$.If we change the angle of incidence to $i = 50^{\circ}$,which is closer to the angle of minimum deviation $(45^{\circ})$ than the initial $53^{\circ}$,the angle of emergence $e$ must also move closer to $45^{\circ}$.Since $37^{\circ} Among the given options,$40^{\circ}$ and $42^{\circ}$ are possible. However,based on the standard behavior of the $i-e$ curve,as $i$ decreases from $53^{\circ}$ to $50^{\circ}$,$e$ increases from $37^{\circ}$. The value $40^{\circ}$ is the most appropriate choice consistent with the deviation properties.

$A$ ray is incident at an angle of $53^{\circ}$ on a prism and emerges at an angle of $37^{\circ}$ as shown. If the angle of incidence is changed to $50^{\circ}$,which of the following is a possible value of the angle of emergence (in $^{\circ}$)?

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