Question

When a small lamp is held $1.5m$ above the surface of the water in a tank, its image formed by reflection at the surface appears to coincide with the image of the bottom of the tank. ($\mu$ of water =1.33)
The depth of the tank is

• A. $2m$
• B. $1.5m$
• C. $1m$
• D. $4m$

Answer 1

Answer: (A)

$2m$

It is given that the lamp is held $1.5m$ above surface of the water. Since it undergoes reflection, the depth of image also appears to be at $1.5m$ below the water surface.

Hence, apparent depth $d=1.5m$

Refractive index of water $\mu =1.33$

We know the relation $\mu =\frac{D}{d}$ where $D=$real depth.

$\therefore D=\mu \times d$

$\Rightarrow D=1.5\times 1.33=1.995m$

Therefore the depth of the tank is almost equal to $2m$.

Hence the correct answer is option (A).