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: Recall the four standard image cases for a convex lens.
When the object is at infinity the image sits exactly at the focus $F_2$. When the object is beyond $2F_1$ the image lies between $F_2$ and $2F_2$, real, inverted and smaller. When the object is between $F_1$ and $2F_1$ the image lies beyond $2F_2$, real, inverted and larger. When the object is exactly at $F_1$ the rays leave the lens parallel, so the image forms at infinity.
Step 2: Match each numbered object position with its lettered image.
Position 1, at infinity, pairs with the image at $F_2$, position 2, beyond $2F_1$, pairs with the image between $F_2$ and $2F_2$, position 3, between $F_1$ and $2F_1$, pairs with the image beyond $2F_2$, and position 4, at $F_1$, pairs with the image at infinity.
Step 3: Write these as the option code.
Using the lettering in the figure, this comes out as $1$ to $D$, $2$ to $A$, $3$ to $B$, and $4$ to $C$.
Step 4: Pick the matching option.
Comparing this sequence with the given choices, it is exactly the second option in the list.
\[ \boxed{1\text{-}D,\ 2\text{-}A,\ 3\text{-}B,\ 4\text{-}C} \]