Question

When distance between object and screen is more than 4 times the focal length, in how many positions of the convex lens, image is sharp ?

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The Correct Option is B

To solve this problem, we need to determine how many positions of a convex lens will produce a sharp image on a screen, given that the distance between the object and the screen is more than four times the focal length of the lens.

1. Lens Formula:
The lens formula is: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] Where:
\( f \) = focal length,
 \( v \) = image distance from the lens, and
\( u \) = object distance from the lens.

2. Using Optical Bench Concept:
If the distance between the object and the screen (let's call it \( D \)) is fixed and \( D > 4f \), then there are exactly **two** positions of the convex lens where a sharp image can be formed on the screen.
These positions are symmetrical with respect to the center of the distance \( D \), and one gives a magnified image while the other gives a diminished image.

3. Condition for Two Positions:
Two positions for a sharp image are possible only if: \[ D > 4f \] This is given in the question, so the condition is satisfied.

Final Answer:
The correct answer is (B) 2.