The convex surface of a thin concavo-convex lens of glass of refractive index 1.5 has a radius of curvature 20 cm. The concave surface has a radius of curvature 60 cm. The convex side is silvered and placed on a horizontal surface as shown in figure (18-E13). (a) Where should the pin be placed on the axis so that its image is formed at the same place? (b) If the concave part is filled with water (μ =4/3), find the distance through which the pin should be moved so that the image of the pin again coincides with the pin.
(a) Let F be the focal length of the given concavo-convex lens.
Then,
--------------- (i)
The value of 
can be obtained by using lens makers’ formula:
Substituting these values in equation (i):
F=
For the image to be informed at the same point as the object
u = 2F = 2 x 7.5 = 15 cm.
Therefore, the pin should be placed at a distance of 15 cm from the lens.
(b) If the concave part is filled with water;
If 
is the focal length of lens in water, the focal length F’ of this combination is given by:
----------------------- (ii)
The value of 
is calculated by Lens makers’ formula:
⇒ 
⇒ 
Substituting these values in equation (ii):
u’ = 2F= 2× 
=
cm
Displacement of pin = u-u’ =
(towards the lens).