Question

Match the positions of the object (Column A) with the corresponding positions of the image formed by a convex lens (Column B).

• A. 1-A, 2-B, 3-C, 4-D
• B. 1-D, 2-A, 3-B, 4-C
• C. 1-B, 2-A, 3-D, 4-C
• D. 1-C, 2-D, 3-A, 4-B

Hint:

Object and image positions show a reciprocal relationship:
- Object at infinity \(\to\) Image at focus.
- Object at focus \(\to\) Image at infinity.
- Object beyond \(2F\) \(\to\) Image between \(F\) and \(2F\).
- Object between \(F\) and \(2F\) \(\to\) Image beyond \(2F\).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks to match different positions of an object in front of a convex (converging) lens with the corresponding positions where its image is formed.

Step 2: Key Formula or Approach:
We use the standard image formation rules for a convex lens.

Step 3: Detailed Explanation:

• Let us analyze each case:
- 1. At infinity: Rays of light coming from infinity are parallel to the principal axis and converge at the principal focus (\(F_2\)) of the lens after refraction. Thus, 1 matches with D.
- 2. Beyond \(2F_1\): When the object is placed beyond twice the focal length, the refracted rays converge to form a real, inverted, and diminished image between the focus (\(F_2\)) and twice the focal length (\(2F_2\)) on the other side. Thus, 2 matches with A.
- 3. Between \(F_1\) and \(2F_1\): When the object is placed between \(F_1\) and \(2F_1\), the image is formed beyond \(2F_2\) on the other side. The image is real, inverted, and magnified. Thus, 3 matches with B.
- 4. At focus \(F_1\): When the object is placed exactly at the principal focus \(F_1\), the refracted rays travel parallel to each other and meet at infinity. Thus, 4 matches with C.

• Combining these matches: 1-D, 2-A, 3-B, and 4-C.


Step 4: Final Answer:
The correct matching option is (B).