Question

3. A stone placed at bottom of a water tank appears to be raised by 80 cm. If the RI of water is 4/3, find the actual depth of the water tank.

Answer 1

$\large{\red{ \bf{ \underline {\underline{Answer}}}}} \\ \\ \purple{ \sf{\mapsto The \: actual \: depth \: of \: water \: tank = 320 \: cm}} \\ \\ \mathrm{\green{ \underline{Given}}} \\ \\ \sf{ \rightsquigarrow Appears \: raised = 80 \: cm} \\ \\ \sf{ \rightsquigarrow Reflection \: index \: (RI) = \frac{ \: 4 \: }{ \: 3 \: } }\\ \\ \mathrm {\blue{ \underline{ To \: Find}}} \\ \\ \sf{ \rightsquigarrow Actual \: depth\:of\:water\:tank\:=\:?}$

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❏ According To Given Question

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$\sf{Let \: the \: real \: depth \:of \: tank \: be \: x} \\ \\ \sf{Apparent \: thickness =(x-80) \: cm} \\ \\ \sf{: \implies \mu = \frac{Real \: depth}{Apparent \: thickness} } \\ \\ \sf{ : \implies \frac{4}{3} = \frac{x}{x - 80} } \\ \\ \sf{ : \implies 4x - 320 = 3x} \\ \\ \sf{ : \implies 4x - 3x = 320} \\ \\ \sf{ \purple{ : \implies \underline{ \boxed{ \sf{x = 320 \: cm}}}}}$

$\sf{\purple{\therefore\:Hence, \:the\:actual\:depth\:of\: water \:tank=320\:cm}}$