A cubical vessel has opaque walls. An observer (dark circle in figure below) is located such that she can see only the wall CD but not the bottom. Nearly to what height should water be poured so that she can see an object placed at the bottom at a distance of $10 \mathrm{~cm}$ from the corner $\mathrm{C}$ ? (Refractive index of water is $1.33$.

• A

  $10 \mathrm{~cm}$
• B

  $16 \mathrm{~cm}$
• Correct answer
  C

  $27 \mathrm{~cm}$
• D

  $45 \mathrm{~cm}$

Solution

$\mu \sin i=1 \cdot \sin 45^{\circ}$ $\frac{4}{3} \sin i=\frac{1}{\sqrt{2}}$ $\frac{4}{3} \frac{y-10}{\sqrt{(y-10)^{2}+y^{2}}}=\frac{1}{\sqrt{2}}$ $y=27$ (approximate calculation)

Hence, the correct answer is option: 'C'.