Question

a biconcave lens made of a transparent material of refractive index 1.25 is immersed in water of refractive index 1.33. will the lens behave as a converging or diverging lens? give reason.

Answer 1

As lens is less optically dense than water,  it will behave as a converging lens.  It will change its behaviour from concave to convex.

if the ratio, of the refractive index of the lens and the medium around it , is more than 1 then the lens will behave as a concave lens.

if the ratio is less than 1, then the lens will behave as  a  convex lens.
 
the lens makers formula for the concave lens is given by :

           1/f =  (n2 / n1 - 1) [- 2 / R ]

   f = focal length,    n2 = refractive index of the medium of lens.
    n1 = refractive index of medium around the lens
  R = radius of curvature of the lens surfaces.

HERE, if  n2 > n1  ,  then  f = negative.  so  it is a concave lens.  The rays diverge from the lens.  This is  because the angle of incidence/refraction in the medium 1 is more than that of lens medium.  The rays bend towards normal in the lens.

if  n2 < n1 ,  then then the lens will act as a convex lens.  It is because, the rays bend away from the normal and converge towards the principal axis.

Answer 2

the refractive index of the lens is lesser than then the refractive index of medium i.e. water so it will behave like diverging lens.