Question

A equiconvex lens is cut into two halves along (i) XOX and (ii)YOY as shown in the figure. Let f,ff 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

• A. f'=f, f"=2f
• B. f'=2f, f"=f
• C. f'=f, f"=f
• D. f'=2f, f"=2f

Answer 1

The Correct Option is A

To solve this problem, we need to consider the optical properties of the equiconvex lens when it is cut along different axes. Let's analyze each case separately:

1. Case (i) - Cutting along XOX:
   • When the lens is cut along the horizontal axis (XOX), the two halves are still segments of the original equiconvex lens. Each half will act like a plano-convex lens.
   • The focal length of a plano-convex lens remains the same as that of the equiconvex lens from which it was derived. Therefore, the focal length f' of each half in this case remains f.
2. Case (ii) - Cutting along YOY:
   • Cutting along the vertical axis (YOY) results in each half having only one of the original lens's surfaces. This effectively reduces the curvature of the lens.
   • When the curvature is reduced by half, the focal length f'' is doubled. Therefore, f'' = 2f.

Based on these analyses, we can choose the correct option:

• f' = f, f'' = 2f

This explanation aligns with the provided correct answer.