A fish in a pond at a depth $d_1=30\text{ cm}$ looks up at a bird flying at a height $h=30\text{ cm}$ above the water surface. What is the apparent distance of the bird as seen by the fish? (Refractive index of water $\mu =4/3$)

Solution

1. Given the depth of the fish $d_1=30\text{ cm}$, the height of the bird $h=30\text{ cm}$, and the refractive index of water $\mu =4/3$.
2. The apparent height $h^{\prime }$ of the bird as seen by the fish is given by $$\begin{array}{rl}{h}^{\prime }& =\mu \times h\\ & =(4/3)\times 30\text{ cm}\\ & =40\text{ cm}\end{array}$$.
3. The total apparent distance is the sum of the fish's depth and the bird's apparent height: $$\begin{array}{rl}{d}_{total}& =d_1+h^{\prime }\\ & =30\text{ cm}+40\text{ cm}\\ & =70\text{ cm}\end{array}$$.
4. Hence the answer is (B).