Question

2) A tank depth is 2d and the apparent depth of the liquid in the tank is 60% its actual depth. What is the refractive index of the liquid with respect to air? [1.67]

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Apparent}\mathrm{depth}=\frac{\mathrm{Real}\mathrm{depth}}{\mathrm{Refravtive}\mathrm{index}\mathrm{of}\mathrm{the}\mathrm{medium}} \\ \mathrm{Real}\mathrm{depth}=2\mathrm{d} \\ \mathrm{apparent}\mathrm{depth}=60\%\mathrm{of}2\mathrm{d} \\ \mathrm{apparent}\mathrm{depth}=\frac{60}{100}\times 2\mathrm{d}=\frac{6\mathrm{d}}{5} \\ \mathrm{Refravtive}\mathrm{index}\mathrm{of}\mathrm{the}\mathrm{medium}=\frac{\mathrm{Real}\mathrm{depth}}{\mathrm{Apparent}\mathrm{depth}} \\ \mathrm{Refravtive}\mathrm{index}\mathrm{of}\mathrm{the}\mathrm{medium}=\frac{2\mathrm{d}}{{\displaystyle \raisebox{1ex}{$6\mathrm{d}$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}} \\ \mathrm{Refravtive}\mathrm{index}\mathrm{of}\mathrm{the}\mathrm{medium}=\frac{5}{3}=1.67 \end{gathered}$$