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Question

When a convex lens produces a real image of an object, the minimum distance between the object and image is equal to ________.

This question was previously asked in
CDS I 2018 Elementary Mathematics Previous Year Paper (04-Feb-2018)
The correct answer is

four times the focal length of the convex lens

Correct Answer

Option 3: four times the focal length of the convex lens

Simplified Solution

1. Understanding the Setup

Let \(f\) be the focal length of the convex lens.

Let \(u\) be the object distance from the lens.

Let \(v\) be the image distance from the lens.

The total distance between the object and the real image is \(D = u + v\).

2. Finding the Minimum Distance

A convex lens forms a real, inverted, and same-sized image when the object is placed exactly at twice the focal length (\(2f\)).

Therefore, the object distance is: \(u = 2f\)

The resulting image distance on the other side is: \(v = 2f\)

3. Final Calculation

Total Minimum Distance = \(u + v\)

Total Minimum Distance = \(2f + 2f = 4f\)

Conclusion: The minimum distance between an object and its real image for a convex lens is always equal to four times the focal length (\(4f\)).

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