Question

When object moves closer to convex lens, the image formed by it shifts :

• A. away from the lens.
• B. towards the lens.
• C. first towards and then away from the lens.
• D. first away and then towards the lens.

Hint:

For a real image in a convex lens, as the object moves closer to the lens, the image always moves away from the lens.
They move in the same absolute direction along the axis.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks about the direction in which the image shifts when an object is brought closer to a convex lens from a distance.

Step 2: Key Formula or Approach:
We use the lens formula to track the position of the image:
\[ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \implies \frac{1}{v} = \frac{1}{f} + \frac{1}{u} \]

Step 3: Detailed Explanation:

• Let us trace the positions step-by-step as the object is moved closer to the lens:
- When the object is at infinity (\(u = -\infty\)), the image is formed at the focus \(F_2\) (\(v = f\)).
- As the object is brought closer, say beyond \(2F_1\), the image shifts to a position between \(F_2\) and \(2F_2\).
- When the object reaches \(2F_1\) (\(u = -2f\)), the image moves to \(2F_2\) (\(v = 2f\)).
- When the object is between \(F_1\) and \(2F_1\), the image shifts beyond \(2F_2\).
- When the object is at the focus \(F_1\) (\(u = -f\)), the image shifts to infinity (\(v = \infty\)).

• Throughout this entire range (from infinity to the focus), as the object distance \(|u|\) decreases, the image distance \(v\) increases.

• This means the image moves further away from the lens.


Step 4: Final Answer:
The image shifts away from the lens.