An equiconvex lens is cut into two halvesalong(i) XOX′ and(ii) YOY′ as shown in the figure. Let f,f′,f" be the focal lengths of the complete lens, of each half in case (i), and of each half in case (ii), respectively. Choose the correct statement from the following
since the lens is equiconvex, the radius of curvature of each half is same, say R. We know from Lens maker's formula
1
f
=(µ−1)(
1
R1
−
1
R2
) (considering the lens to be placed in air). Here R1=R R2=−R by convention ∴
1
f
=(µ−1)
2
R
⇒(µ−1)
1
R
=
1
2f
......(i) If we cut the lens along XOXprime then the two halves of the lens will be having the same radii of curvature and so, focal length f′=f But when we cut it along YOY′ then, we will have R1=R‌but‌R2=∞ ∴