Question

In a science-fiction novel, an intelligent ocean-dwelling creature's eye functions underwater with a near point of 27 cm . This creature would like to create an underwater magnifier out of a thin plastic container filled with air.

Part A

What shape should the air-filled plastic container have (i.e., determine radii of curvature of its surfaces) in order for it to be used by the creature as a 4.0 × magnifier? Assume the eye is focused at its near point.

Express your answer using two significant figures.

R=

  

cm

Answer 1

As eye is focussed at near point, image formed by plastic container should be at distance of 27 cm from itself.
Magnification = NP/do
=> 4 = 27/do
distance of object from container do = 27/4 cm
Image formed by container is virtual, so di = -27 cm
1/di + 1/do = (na/nw -1)(2/R)
na is refrective index of air = 1
nw is refrective index of water = 4/3
R is radius of curvature of surfaces
1/-27 cm + 4 / 27cm = (3/4 -1) 2/R
R = - 4.5 cm
-ve sign indicates surfaces are concave towards water.