Question

This question has multiple correct options

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Solution

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Correct options are A) , C) and D)

We know for minimum deviation, $i_{1}=2A+δ_{m} $( $δ_{m}$ : angle of minimum deviation)

Given $δ_{m}=A$

Hence $i_{1}=A$

Now, for minimum deviation condition $r_{1}=A/2$

Hence $r_{1}=i_{1}/2$

$Correct$

$OptionB$

$μ=sin(r_{1})sin(i_{1}) $

$μ=Sin(A/2)sin(2A+δ_{m} ) $

$μ=sinA/2sinA $ = $2cosA/2$

$Incorrect$

$OptionC$

Emergence = $90_{o}$

$sinr_{2}=μ$

$r_{2}=Sin_{−1}μ$

Also $r_{1}=A−r_{2}$

$sini_{1}=μsinr_{1}$

$sini_{1}=μsin(A−r_{2})$

$sini_{1}=μ(sinAcosr_{2}−cosAsinr_{2})$

But $μsinr_{2}=1$

$sini_{1}=μsinAcosr_{2}−cosA$= $sinA4cos_{2}A/2−1 −cosA$

$Correct$

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