Question
A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is $$\frac{4}{3}$$ and the fish is $$12\,cm$$ below the surface, the radius of this circle (in $$cm$$ ) is -
A.
$$36\sqrt 5 $$
B.
$$4\sqrt 5 $$
C.
$$36\sqrt 7 $$
D.
$$\frac{{36}}{{\sqrt 7 }}$$
Answer :
$$\frac{{36}}{{\sqrt 7 }}$$
Solution :
$$\eqalign{ & \sin {i_c} = \frac{1}{\mu } = \frac{r}{{\sqrt {{r^2} + {h^2}} }} \cr & {\text{Using}}\,\,h = 12\,cm,\mu = \frac{4}{3} \cr & {\text{We}}\,{\text{get}}\,\,r = \frac{{36}}{{\sqrt 7 }}cm. \cr} $$
$$\eqalign{ & \sin {i_c} = \frac{1}{\mu } = \frac{r}{{\sqrt {{r^2} + {h^2}} }} \cr & {\text{Using}}\,\,h = 12\,cm,\mu = \frac{4}{3} \cr & {\text{We}}\,{\text{get}}\,\,r = \frac{{36}}{{\sqrt 7 }}cm. \cr} $$
