A lens is a transparent optical medium bounded by two surfaces; at least one of which should be spherical. Considering image formation by a single spherical surface successively at the two surfaces of a lens, lens maker's formula is obtained. It is useful to design lenses of desired focal length using surfaces of suitable radii of curvature. This formula helps us obtain a relation between u, v and f for a lens. Lenses form images of objects and they are used in a number of optical devices, for example microscopes and telescopes. (i) An object AB is kept in front of a composite convex lens, as shown in figure. Will the lens produce one image ? If not, explain. (ii) A real image of an object formed by a convex lens is observed on a screen. If the screen is removed, will the image still be formed ? Explain. (iii) A double convex lens is made of glass of refractive index 1.55 with both faces of the same radius of curvature. Find the radius of curvature required if focal length is 20 cm. (iii) Two convex lenses A and B of focal lengths 15 cm and 10 cm respectively are placed coaxially 'd' distance apart. A point object is kept at a distance of 30 cm in front of lens A. Find the value of 'd' so that the rays emerging from lens B are parallel to its principal axis.

PhysicsCBSE Class 12 · Board exam 2023, set 55/5/1 · 4 marks · Case-based

CBSE Class 12 Physics 2023: question 34

Set in the CBSE Class 12 board exam of 2023, paper 55/5/1, section E, question 34, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q34 · 4 marks · Case-basedCompetency-basedRay Optics and Optical Instruments

A lens is a transparent optical medium bounded by two surfaces; at least one of which should be spherical. Considering image formation by a single spherical surface successively at the two surfaces of a lens, lens maker's formula is obtained. It is useful to design lenses of desired focal length using surfaces of suitable radii of curvature. This formula helps us obtain a relation between u, v and f for a lens. Lenses form images of objects and they are used in a number of optical devices, for example microscopes and telescopes.

(i)
An object AB is kept in front of a composite convex lens, as shown in figure. Will the lens produce one image ? If not, explain.
0 marks
(ii)
A real image of an object formed by a convex lens is observed on a screen. If the screen is removed, will the image still be formed ? Explain.
0 marks
(iii)
A double convex lens is made of glass of refractive index 1.55 with both faces of the same radius of curvature. Find the radius of curvature required if focal length is 20 cm.
0 marks
OR
(iii)
Two convex lenses A and B of focal lengths 15 cm and 10 cm respectively are placed coaxially 'd' distance apart. A point object is kept at a distance of 30 cm in front of lens A. Find the value of 'd' so that the rays emerging from lens B are parallel to its principal axis.
0 marks

Figure in the paper: Object AB (upright arrow, A top, B bottom on the principal axis) in front of a convex lens whose upper half has refractive index n1 and lower half has n2 (split along the principal axis). See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 55/5/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

The focal length of a lens depends on its refractive index; think about what happens when two parts of one lens have different $n$ .

Hint 2

A real image is the point where rays actually meet; ask whether that depends on a screen being present.

Hint 3

For (iii), set $R_{1} = R$ and $R_{2} = - R$ in the lens maker's formula. For the OR part, rays emerge parallel when the intermediate image lies at the focus of the second lens.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

(i) No, the lens will not produce a single image. The upper and lower halves have different refractive indices $n_{1}$ and $n_{2}$ . By the lens maker's formula, each half therefore has a different focal length, so the two halves form two separate images of AB.
1 mark
(ii) Yes, the image is still formed. A real image exists wherever the refracted rays actually meet, whether or not a screen is placed there. The screen only makes the image visible.
1 mark
(iii) Lens maker's formula. $\frac{1}{f} = (n - 1) (\frac{1}{R _{1}} - \frac{1}{R _{2}})$ . For a double convex lens with equal radii, $R_{1} = + R$ and $R_{2} = - R$ .
½ mark
Simplifying. $\frac{1}{f} = \frac{2 ( n - 1 )}{R}$ , so $R = 2 (n - 1) f$ .
½ mark
Substituting. $R = 2 (1.55 - 1) \times 20 = 2 \times 0.55 \times 20 = 22$ cm.
1 mark
(iii) OR alternative (2 marks if this choice is attempted). For lens A, $u = - 30$ cm and $f = 15$ cm. From $\frac{1}{v} = \frac{1}{f} + \frac{1}{u} = \frac{1}{15} - \frac{1}{30} = \frac{1}{30}$ , we get $v_{1} = 30$ cm behind A.
For the rays from B to come out parallel to the principal axis, the image formed by A must lie at the focus of B, i.e. 10 cm in front of B. Hence $d = 30 + 10 = 40$ cm.

Answer: (i) No, two images form because the halves have different focal lengths; (ii) Yes, the image is still formed; (iii) R = 22 cm [OR d = 40 cm]

Where the marks are

(i) Says no and explains that the two refractive indices give two focal lengths and hence two images (½ + ½ mark)
(ii) Says yes and explains that the rays still converge at the image position (½ + ½ mark)
(iii) Applies the lens maker's formula with $R_{1} = R$ , $R_{2} = - R$ to get $R = 2 (n - 1) f$ (1 mark)
(iii) Obtains R = 22 cm (1 mark)
(iii) OR: Finds $v = 30$ cm for lens A (1 mark), then uses the focus of B to get d = 40 cm (1 mark)

Revise the chapter

Chapter: Ray Optics and Optical Instruments (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Ray Optics and Optical Instruments, one at a time, marked against the answer key and marking points.Back to the full paper2023 board paper, set 55/5/1: every question, by section.

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CBSE Class 12 Physics 2023: question 34

Hints

Step-by-step solution

Revise the chapter

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