Question

A fish at the bottom of a pond appears to be 1.2 m from the water surface. What is the depth

of the pond?

(a) 1.67 (b) 1.85 (c) 1.78 (d) 1.59​

Answer 1

Given:

A fish at the bottom of a pond appears to be 1.2 m from the water surface.

To find:

Depth of pond?

Calculation:

So, in the question, the depth at which the fish is seen is actually the apparent depth. Apparent depth is slightly above the actual depth (due to refraction at water-air interface.

$\rm \therefore \: d_{apparent} = \dfrac{ d_{actual} }{ \mu}$

$\rm \implies\: d_{actual} =d_{apparent} \times \mu$

$\rm \implies\: d_{actual} =1.2 \times 1.33$

$\rm \implies\: d_{actual} \approx 1.59 \: m$

So, actual depth of pond is 1.59 metres.

Answer 2

$\huge{\underline{\sf Solution:-}}$

Here

• $\sf Apparent\:death=d_{apparent}=1.2m$
• $\sf Refractive\:index\:of\:water=\mu=1.33$

We know that

$\boxed{\sf d_{apparent}=\dfrac{d_{actual}}{\mu}}$

$\\ \sf\bull\rightarrowtail 1.2=\dfrac{d_{actual}}{1.33}$

$\\ \sf\bull\rightarrowtail d_{actual}=1.2\times 1.33$

$\\ \sf\bull\rightarrowtail\underline {\boxed{\bf{ d_{actual}\approx 1.59m}}}$

Thus option D is correct.