If a symmetrical bi-concave thin lens is cut into two identical halves, and they are placed in different ways as shown, then

Options

A. three images will be formed in case (ii)
B. three images will be formed in case (i)
C. the ratio of focal lengths in (ii) and (iii) is 1
D. the ratio of focal lengths in (ii) and (iii) is 2

Answer

C

Explanation

(a) Two images are formed in case(i).
(b) One image is formed in case (ii).
(c) `1/(f_2)=(mu-1)(1/(-R)-1/R)=-2/R(mu-1)….(i)`
`1/(f_3)=1/(F_1)+1/(F_2)`
`=(mu-1)(1/oo-1/R)+(mu-1)(1/(-R)-1/oo)…..(ii)`
From Eqs. (i) and (ii), we can see that `f_2=f_3.`