question_answer

An equiconvex lens is cut into two halves along (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:                                                     [AIPMT 2003]

A)              \[f'=f,\,\,f''=f\]

B)       \[f'=2f,\,\,f''=2f\]

C)              \[f'=f,\,\,f''=2f\]

D)       \[f'=2f,\,\,f''=f\]

Correct Answer: C

Solution :

Initially, the focal length of equiconvex lens is                          ....(i)

Case I: When lens is cut along XOX', then each half is again equiconvex with

Thus,

Case II: When lens is cut along YOY', then each half becomes plano-convex with

Thus,

Hence,