Question

In a thin spherical fish bowl of radius `10` cm filled with water of refractive index `(4//3)` , there is a small fish at a distance `4` cm from the centre `C` as shown in Figure. Where will the fish appear to be, if seen from (a) `E` and (b) `F` (neglect the thickness of glass)?

Answer 1

In the case of refraction from curved surface `(mu_(2))/(v) - (mu_(1))/(u) = ((mu_(2) - mu_(1))/(R)`
(a) Seen from `E mu_(1) = (4)/(3), mu_(2) = 1, R = -10 "cm"` & `u = -(10-4) = -6"cm"`
`implies (1)/(v) - ((4)/(3))/(-6) = (1-(4)/(3))/(-10) implies v= (90)/(17) = -5.3"cm"`
i.e., fish will appear at a distance `5.3` cm from `E` towards `F` (lesser than actual distance i.e., `6` cm)
(b) Seen from `F mu_(1) = (4)/(3) , mu_(2) = 1 , R=-10 "cm and" u=-(10+4)=-14"cm"`
`implies (1)/(v) - ((4)/(3))/(-14) = (1-(4)/(3))/(-10) implies v= (-210)/(13) = -16.154"cm"`
so fish will appear at a distance `16.154` cm from `F` toward `E` (more than actual distance , i.e., `14` cm)