Question

A far away object approaches a convergent lens from the left with a uniform speed of $5~m/s$ and stops at the focus. During this time the image on the right moves:

• A. away from the lens with an uniform speed of $5~m/s.$
• B. away from the lens with an uniform acceleration.
• C. away from the lens with a non-uniform acceleration.
• D. towards the lens with a non-uniform acceleration.

Hint:

As an object gets closer to a convex lens, the image runs away faster and faster!

Answer 1

The Correct Option is C

Step 1: Concept
For a convergent (convex) lens, the image position ($v$) changes as the object position ($u$) changes according to the lens formula: $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$.

Step 2: Analysis of Movement
When the object is at infinity, the image is at the focus ($F$). As the object moves toward $F$ from the left, the real image moves from $F$ toward infinity on the right.

Step 3: Reasoning
The relationship between $v$ and $u$ is non-linear. Even if the object speed is uniform, the rate of change of image position ($\frac{dv}{dt}$) is not constant and not a linear function of time, implying non-uniform acceleration.

Step 4: Conclusion
The image moves away from the lens with a non-uniform acceleration. Final Answer: (C)