The convex surface of a thin concave-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. (a) Where should a 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 (mu = 4/3), find the distance through which the pin should be moved so that the image of the pin again coincides with the pin.

Explanation

Let F is the focal length of given cncave convex lens. Then
`1/F=1/f_1+1/f_m+1/f_1`
`=2/f_1+1/f_m`
`[:' 1/f_m=(mu-1)(1/R_1-1/R_2)]`

`=2/30+1/15=2/15`
`rarr F=7.5cm`
Hence R=15cm
Therefore pin should be placed 15cm from the lense.
b. When water is filled in concasve part.
for focal length F'
`1/F'=2/F_2=2/F_1+1/F_m`
`=2/90+2/30+1/15`
`[:'1/F_w=(4/3-1)(+1/30)]`
`:.F'=45/7cm`
so, pin shoud be placed at 90/7 cm from the lens.