At what distance should an object be placed from a convex lens of focal length 18 cm to obtain an image at 24 cm from it on the other side. What will be the magnification produced in this case ?

Light — Reflection and Refraction

Lens Formula and Magnification

Official Answer

The object should be placed at a distance of $72\text{ cm}$ in front of the convex lens. The magnification produced in this case is $-\frac{1}{3}$ (or approximately $-0.33$ ), indicating that the image is real, inverted, and diminished.

Lens formulaObject distanceMagnificationReal and invertedDiminished

Marking Scheme

1Correct application of Lens Formula with sign convention (1 mark)
2Calculation of object distance ( $u = -72\text{ cm}$ ) (1 mark)
3Calculation of magnification ( $m = -1/3$ ) (1 mark)

Hint

Use the lens formula $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$ and remember that for a convex lens, $f$ is positive and a real image on the other side means $v$ is positive.

Quick Oral Answer

The negative sign of magnification indicates that the image is real and inverted. A value less than 1 (like 1/3) means the image is smaller than the object.

Analysis & Explanation

According to the Cartesian sign convention, the focal length of a convex lens is positive. Since the image is formed on the other side of the lens, it is a real image, making the image distance ( $v$ ) positive. The lens formula relates the focal length, object distance, and image distance. Solving this gives a negative object distance, which is consistent with the object being placed in front of the lens. The negative sign in magnification confirms the image is inverted.

Common Mistakes

1Using the mirror formula instead of the lens formula.
2Incorrect sign for focal length (taking it as negative).
3Forgetting that magnification for lenses is $v/u$ , not $-v/u$ .

Interesting Facts

A convex lens can form both real and virtual images depending on the object position, but if the image is on the 'other side', it is always real.

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Frequently Asked Questions

How many marks does this question carry in CBSE Class 10 Science 2010?

This question carries 3 marks in the CBSE Class 10 Science 2010 examination.

Which chapter does this question come from in Science?

This question is from the chapter "Light — Reflection and Refraction" in the CBSE Class 10 Science syllabus.

What topic does this question cover in Science?

This question covers the topic "Lens Formula and Magnification" from CBSE Class 10 Science.

What type of question is this in the CBSE Class 10 Science 2010 paper?

This is a Short Answer question from Section A in the CBSE Class 10 Science 2010 paper.