An equilateral prism deviates a ray through 4 | vedclass

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Question

(A) For a prism,the deviation formula is $\delta = i + e - A$.Given,$\delta = 40^{\circ}$ and $A = 60^{\circ}$ (equilateral prism).So,$40^{\circ} = i

Vedclass · Accepted Answer

$40^{\circ}, 60^{\circ}$

Vedclass · Answer

(A) For a prism,the deviation formula is $\delta = i + e - A$.Given,$\delta = 40^{\circ}$ and $A = 60^{\circ}$ (equilateral prism).So,$40^{\circ} = i + e - 60^{\circ}$,which implies $i + e = 100^{\circ}$.We are also given that the two angles of incidence differ by $20^{\circ}$,so $|i - e| = 20^{\circ}$.Solving the system of equations:$1$) $i + e = 100^{\circ}$$2$) $i - e = 20^{\circ}$ or $e - i = 20^{\circ}$Adding the equations: $2i = 120^{\circ} \implies i = 60^{\circ}$.Substituting back: $60^{\circ} + e = 100^{\circ} \implies e = 40^{\circ}$.Thus,the two possible angles of incidence are $60^{\circ}$ and $40^{\circ}$.

An equilateral prism deviates a ray through $40^{\circ}$ for two angles of incidence differing by $20^{\circ}$. The possible angles of incidence are:

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