Question

A convex lens of focal length $\frac{1}{3} \text{ m}$ forms a real, inverted image twice the size of the object. The distance of the object from the lens is

• A. 0.5 m
• B. 0.166 m
• C. 0.33 m
• D. 1 m

Hint:

For a convex lens, real images mean the object is beyond the focal point.

Answer 1

The Correct Option is A

Step 1: Concept
Magnification $m = v/u$. For a real, inverted image, $m$ is negative.

Step 2: Meaning
Given $m = -2$, so $v = -2u$. By sign convention, $u$ is negative, so $v = 2|u|$.

Step 3: Analysis
Use lens formula: $1/f = 1/v - 1/u$. $1/(1/3) = 1/(-2u) - 1/u \implies 3 = -1/2u - 2/2u \implies 3 = -3/2u$. Solving for $u$: $2u = -1$, so $u = -0.5 \text{ m}$.

Step 4: Conclusion
The object distance is $0.5 \text{ m}$ from the lens. Final Answer: (A)