An object of height 4.0 cm is placed at a distance of 30 cm from the optical centre ‘O’ of a convex lens of focal length 20 cm. Draw a ray diagram to find the position and size of the image formed. Mark optical centre ‘O’ and principal focus ‘F’ on the diagram. Also find the approximate ratio of size of the image to the size of the object.

Light — Reflection and Refraction

Refraction by Spherical Lenses

Official Answer

The image is formed at a distance of $60\text{ cm}$ on the other side of the lens. The size of the image is $8.0\text{ cm}$ (inverted), and the ratio of the size of the image to the size of the object is $2:1$ (or $2$ ).

lens formulav = 60 cmh' = -8.0 cmratio 2:1optical centre Oprincipal focus Freal and inverted

Marking Scheme

1Using lens formula correctly to find image distance $v = +60\text{ cm}$ (0.5 marks)
2Calculating image height $h' = -8.0\text{ cm}$ and the ratio of sizes as $2:1$ (or $2$ ) (0.5 marks)
3Drawing a correct ray diagram with arrows showing direction of light rays (0.5 marks)
4Correctly labeling optical centre 'O' and principal focus 'F' on the diagram (0.5 marks)

Hint

Apply the lens formula $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ with proper sign conventions ( $u$ is negative, $f$ is positive for a convex lens). Magnification is given by $m = \frac{v}{u} = \frac{h'}{h}$ .

Quick Oral Answer

The lens formula is 1/v - 1/u = 1/f. For a convex lens, the focal length is positive. When an object is placed between F and 2F, its image is formed beyond 2F on the other side, which is real, inverted, and magnified.

Analysis & Explanation

When an object is placed between $F_1$ and $2F_1$ of a convex lens (since $f = 20\text{ cm}$ and $u = -30\text{ cm}$ ), its real, inverted, and magnified image is formed beyond $2F_2$ on the other side of the lens.

The ray parallel to the principal axis passes through the principal focus $F_2$ after refraction.
The ray passing through the optical centre $O$ goes straight without any deviation.
The intersection of these two rays at $60\text{ cm}$ behind the lens determines the position of the inverted image.

Common Mistakes

1Using the mirror formula instead of the lens formula.
2Taking the focal length of the convex lens as negative.
3Forgetting to draw arrows on the rays in the ray diagram.

Interesting Facts

A convex lens is also known as a converging lens because it converges parallel rays of light falling on it to a single point called the focus.

Spotted a mistake or something unclear?

Tell us — we fix reported answers fast.

Frequently Asked Questions

How many marks does this question carry in CBSE Class 10 Science 2018?

This question carries 2 marks in the CBSE Class 10 Science 2018 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 2018 paper?

This is a Short Answer question from Section B in the CBSE Class 10 Science 2018 paper.