Question

A fish looking up through the water sees the outside world in a circular horizon. If the refractive index of water is $4/3$ and the fish is $12m$ below the surface, the radius of the circle in $cm$ is

• A. $36\surd 7$
• B. $\frac{36}{\surd 7}$
• C. $36\surd 5$
• D. $4\surd 5$

Answer 1

The correct option is B $\frac{36}{\surd 7}$

For such a situation, tan(i${}_c$) = R/ H where R is the radius of circular horizon.

Also we know that sin(i${}_c$)=$\frac{u_r}{u_d}=\frac{3}{4}$ which gives tan(i${}_c$)=$\frac{3}{\sqrt{7}}$

And it is given that H=12m

So R=htan(i${}_c$)=$\frac{36}{\sqrt{7}}$