Question

A convergent lens is placed \(40\,\text{cm}\) to the right of a divergent lens of focal length \(15\,\text{cm}\). A parallel beam of light enters the divergent lens from the left, and the beam is again parallel when it emerges from the convergent lens. The focal length of the convergent lens is

• A. \(40\,\text{cm}\)
• B. \(25\,\text{cm}\)
• C. \(55\,\text{cm}\)
• D. \(27.5\,\text{cm}\)

Hint:

If rays emerge parallel from a converging lens, the object for that lens must be located at its focal point. Track the image formed by the first lens carefully and use it as the object for the second lens.

Answer 1

The Correct Option is C

Step 1: Analyze diverging lens behavior.
Parallel rays appear to diverge from focal point: virtual image at 15 cm left of diverging lens.

Step 2: Locate object for converging lens.
Separation = 40 cm, so object distance u = –(40+15) = –55 cm.

Step 3: Apply condition for emergent parallel rays.
Object must be at focal point of converging lens: |u| = f → f = 55 cm.

Step 4: Final Answer:
55 cm.