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Updated on : 2022-09-05

Solution

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Let $α,β,γ$ are the ray angle normal with the principle axis respectively.

then by snell's law

$μ=sinrsini $ ........(1)

but here i and r are the small then we put.

$sini=i$ $sinr=r$ in equation (1)

$μ=ri $

$i=μn$ ...........(2)

now by using exterior angle theorem in $Δ$AOC

$γ=1+a$

$i=γ−α$ .........(3)

now in $Δ$IAC by using exterior angle theorem

$γ=b+r$

$rho=γ−β$ ..........(4)

putting value of i and r in equation (2)

$(γ−α)=μ(γ−β)$ ...........(5)

now angle$=radiusarc $

$α=OPPA $

$β=IPPA $

now $γ=CPPA $

using value of $α,β,γ$ in equation (5)

$PCPA −POPA =μ(PCPA −PIPA )$

$PA(PC1 −PO1 )=m.PA(PC1 −PO1 )$

$PC1 −PO1 =μ(PC1 −PI1 )$ .........(6)

now by using sign convention

$PC=−R$ $PI=V$

$PO=−u$

using these value in equation (6)

$(−R1 )−(−u1 )=μ(R−1 +V1 )$

$R−1 +u1 =μ(R−1 +v1 )$

$R−1 +u1 =Rμ +vμ $

$R−1 +Rμ =vμ −u1 $

$Rμ−1 =vμ −u1 $ |

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