Question 213 marksShort AnswerSection A

A 4 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 24 cm. The distance of the object from the lens is 16 cm. Find the position, size and nature of the image formed, using the lens formula.

Light — Reflection and Refraction
Refraction by Spherical Lenses

Official answer

Using the lens formula, the position of the image is at 48 cm48\text{ cm} on the same side as the object (in front of the lens). The size of the image is 12 cm12\text{ cm}, and its nature is virtual and erect.

Answer keywords:lens formulav = -48 cmmagnificationh' = 12 cmvirtual and erectenlarged

Marking scheme

  1. 1.1.5 marks
  2. 2.1 mark
  3. 3.0.5 marks

Hint

Identify the signs of uu and ff carefully. For a convex lens, ff is positive. Since the object is placed closer than the focal length (16 cm<24 cm16\text{ cm} < 24\text{ cm}), expect a virtual, erect, and enlarged image.

Quick oral answer

The image is formed at 48 cm48\text{ cm} on the same side as the object. It is virtual, erect, and has a height of 12 cm12\text{ cm}, which is three times the size of the object.

Common mistakes

  1. 1.Using the mirror formula (1v+1u=1f\frac{1}{v} + \frac{1}{u} = \frac{1}{f}) instead of the lens formula (1v−1u=1f\frac{1}{v} - \frac{1}{u} = \frac{1}{f}).
  2. 2.Using the wrong sign for magnification in lenses (m=−v/um = -v/u is for mirrors; for lenses, it is m=v/um = v/u).
  3. 3.Taking the focal length of a convex lens as negative.

Analysis and explanation

When an object is placed within the focal length of a convex lens (∣u∣<∣f∣|u| < |f|, here 16 cm<24 cm16\text{ cm} < 24\text{ cm}), the lens acts as a magnifying glass. The refracted rays diverge, and their backward extensions meet to form a virtual, erect, and magnified image on the same side as the object. The calculations perfectly match this physical behavior, yielding a negative image distance (v=−48 cmv = -48\text{ cm}) and a positive magnification (m=+3m = +3).

Interesting facts

This setup represents how a simple magnifying glass works! When you hold a magnifying glass very close to an object (closer than its focal length), you see a giant, upright virtual image of the object.

Question details

Q21 of 41 questions

Board
CBSE
Class
Class 10
Subject
Science
Year
2012
Section
Section A
Marks
3
Type
Short Answer
Chapter
Light — Reflection and Refraction
Topic
Refraction by Spherical Lenses
Bloom's level
Applying
Syllabus topic
Lens formula, magnification, and numerical problems on lenses

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Frequently asked questions

How many marks does this question carry in CBSE Class 10 Science 2012?

This question carries 3 marks in the CBSE Class 10 Science 2012 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 "Refraction by Spherical Lenses" from CBSE Class 10 Science.

What type of question is this in the CBSE Class 10 Science 2012 paper?

This is a Short Answer question from Section A in the CBSE Class 10 Science 2012 paper.