Question

On a bright sunny day, a diver of height $h$ stands at the bottom of a lake of depth $H$. Looking upward, he can see objects outside the lake in a circular region of radius $R$. Beyond this circle he see the images of objects lying on the floor of the lake. If refractive index of water is $4/3$, then the value of $R$ is :

• A. $3(H-h)/\sqrt{7}$
• B. $(H-h)/\sqrt{7/3}$
• C. $3h\sqrt{7}$
• D. $3(H-h)/\sqrt{5/3}$

Answer 1

Answer: (A)

$3(H-h)/\sqrt{7}$

Finding the critical angle

$\frac{4}{3}sinC=1\to SinC=\frac{3}{4}$

using so $tanC=\frac{3}{\sqrt{7}}=\frac{R}{H-h}$

So $R=\frac{3(H-h)}{\sqrt{7}}$