Refraction through a Lens

Q: Name the three principal rays used for a convex lens and state the path of each after refraction.

(a) A ray parallel to the principal axis passes through F2. (b) A ray through the optical centre goes straight on. (c) A ray through F1 emerges parallel to the principal axis.

Q: Where must an object be placed in front of a convex lens to obtain a real, inverted image of the same size? Where is the image?

At 2F1, that is, at a distance 2f from the lens. The image forms at 2F2, at 2f on the other side.

Q: State the position and nature of the image formed by a concave lens for an object anywhere in front of it.

Between the optical centre and F2, which for a concave lens lies on the same side as the object. The image is virtual, erect and diminished.

ICSE Class 10 · Physics · Chapter 5

What this chapter covers

Convex and concave lenses
A lens as a set of prisms
Terms used for lenses
Principal rays and ray diagrams
Images formed by a convex lens
Images formed by a concave lens
Sign convention for lenses
Lens formula and magnification
Power of a lens
Magnifying glass (simple microscope)
Applications of lenses

Key points

A lens is a transparent piece of material bounded by two surfaces, at least one of them curved.
A convex lens is thicker at the middle and converges light; a concave lens is thinner at the middle and diverges light.
A lens acts like a set of prisms: bases towards the middle in a convex lens, bases outwards in a concave lens; the centre acts like a thin glass slab.
Key terms: optical centre O, centres of curvature C₁, C₂, radii of curvature, principal axis, principal foci F₁, F₂, focal plane and focal length f.
The focus of a convex lens is real; the focus of a concave lens is virtual.
Principal rays: parallel to the axis → through (or from) a focus; through O → undeviated; through (or towards) a focus → parallel to the axis.
Convex lens: real, inverted images for objects beyond F₁; a virtual, erect, magnified image for an object between F₁ and O.
Concave lens: always a virtual, erect, diminished image between O and F₂, on the object's side.
New Cartesian sign convention: distances from O; along the incident light positive, against it negative; upward heights positive.
Lens formula: (1)/(v) - (1)/(u) = (1)/(f); magnification m = (h₂)/(h₁) = (v)/(u); negative m means real and inverted, positive m means virtual and erect.
Power P = (1)/(f) with f in metres; unit dioptre (D); positive for convex, negative for concave lenses.
A magnifying glass is a convex lens of short focal length with the object inside F₁; its magnification is read from the ray diagram as image height divided by object height.
Lenses are used in spectacles, cameras, the eye, projectors, photocopiers, microscopes, telescopes, door viewers and spotlights.

Questions answered

Define the focal length of a convex lens. What is its sign under the new Cartesian sign convention?

The focal length of a lens is the distance between its optical centre and a principal focus. For a convex lens it is positive, because the focus where parallel rays actually meet lies on the side towards which the light travels.

Why is a convex lens called a converging lens? Explain using the idea of a lens as a set of prisms.

A convex lens can be imagined as prisms whose bases point towards the middle of the lens. Each prism bends light towards its base, so every ray is bent towards the principal axis and a parallel beam comes together. Hence it converges light.

Why does a ray through the optical centre of a thin lens pass undeviated?

Near the optical centre the two faces of the lens are nearly parallel, so this part acts like a thin glass slab. The emergent ray is parallel to the incident ray, and its sideways shift is negligible for a thin lens, so the ray is taken to go straight through.

Name the three principal rays used for a convex lens and state the path of each after refraction.

(a) A ray parallel to the principal axis passes through F₂. (b) A ray through the optical centre goes straight on. (c) A ray through F₁ emerges parallel to the principal axis.

Where must an object be placed in front of a convex lens to obtain a real, inverted image of the same size? Where is the image?

At 2F₁, that is, at a distance 2f from the lens. The image forms at 2F₂, at 2f on the other side.

State the position and nature of the image formed by a concave lens for an object anywhere in front of it.

Between the optical centre and F₂, which for a concave lens lies on the same side as the object. The image is virtual, erect and diminished.

A lens always gives an erect, diminished image of a book held at any distance. Identify the lens.

A concave lens. A convex lens gives an erect image only when the object is inside F₁, and then the image is magnified, not diminished.

An object is 40 cm from a convex lens of focal length 20 cm. Find the image distance and magnification.

u = -40 cm, f = +20 cm. (1)/(v) = (1)/(20) - (1)/(40) = (1)/(40), so v = +40 cm. m = (v)/(u) = (40)/(-40) = -1. The image is real, inverted and the same size, 40 cm behind the lens.

Past board exam questions

ICSE 2027 sample paper · 1 mark

A concave lens diverges light because its upper and lower parts act as:

inverted prisms
upright prisms
upright and inverted prisms respectively
inverted and upright prisms respectively

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inverted and upright prisms respectively

ICSE 2027 sample paper · 2 marks

(a) A lens is made of two materials of different refractive indices (µ1, µ2) as shown: it is a convex lens whose upper half, above the principal axis, is made of the material of refractive index µ1 and whose lower half, below the principal axis, is made of the material of refractive index µ2. If the rays are coming from a distant object, then how many images will be formed? (b) A glass lens always forms a virtual, erect, and diminished image of an object kept in front of it. Identify the lens.

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(a) 2 images will be formed – the two halves have different refractive indices and hence different focal lengths, so they bring the rays to a focus at two different points. (b) Concave lens.

ICSE 2027 sample paper · 4 marks

A candle and a screen are placed 90 cm apart. Steve placed a lens between them such that a clear image is formed on the screen and the image is twice the size of the object. (a) Which type of lens is used by Steve? (b) Write an equation relating the object distance u, image distance v, and the distance between the candle and the screen. (c) State the ratio between the image distance v and the object distance u. (d) Calculate the image distance.

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(a) Convex lens (a real, magnified image is formed on the screen). (b) v + u = 90 cm (taking magnitudes of the distances). (c) m = −2 (real, inverted image), so v : u = 2 : 1. (d) v = 2u and v + u = 90 → 3u = 90 → u = 30 cm, so the image distance v = 90 − 30 = 60 cm.

ICSE 2027 sample paper · 3 marks

Draw a ray diagram to show the formation of an image by a concave lens when the object is placed between F and 2F.

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Ray diagram: an object AB stands on the principal axis between F and 2F on the left of a concave lens. 1. A ray from B parallel to the principal axis diverges after refraction, appearing to come from the focus F on the object's side (shown by a dotted backward extension). 2. A ray from B towards the optical centre O passes straight through undeviated. The refracted rays, extended backwards, meet at B′. The image A′B′ is formed between F and O on the same side as the object; it is virtual, erect and diminished. Arrows on the rays show their direction.

ICSE 2026 board paper · 1 mark

The distance (V) of a virtual image formed by a lens of focal length 15 cm never exceeds a certain finite value, then this value will be:

less than 15 cm
between 15 cm to 30 cm
less than or equal to 30 cm
less than or equal to 15 cm

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less than or equal to 15 cm

ICSE 2026 sample paper · 1 mark

A convex lens with a focal length of 12 cm has an object at a distance of 20 cm in front of the lens. A blurred image is obtained on the screen placed at a distance of 23 cm in front of the lens. In order to obtain a clear image, the screen has to be moved:

towards the lens.
away from the lens.
to a position very far from the lens.
either towards or away from the lens.

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away from the lens.

ICSE 2026 sample paper · 2 marks

(a) A double convex lens is made of two materials of different refractive indices (µ₁, µ₂): the half of the lens above the principal axis has refractive index µ₁ and the half below the principal axis has refractive index µ₂. If the rays are coming from a distant object, then how many images will be seen? (b) A glass lens always forms a virtual, erect, and diminished image of an object kept in front of it. Identify the lens.

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(a) Two images. The upper half (µ₁) and the lower half (µ₂) have different refractive indices, so they have different focal lengths; rays from a distant object are focused at two different points. (b) A concave lens.

ICSE 2026 board paper · 3 marks

An object placed in front of a convex lens, forms an image of same size on a screen. Moving the object 12 cm closer to the lens results in the formation of a real image which is three times the size of the object. Calculate the focal length of the lens.

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A real image of the same size is formed when the object is at 2F, so the object distance is 2f. New object distance = (2f − 12) cm; the image is real and three times as large, so v = 3 × (2f − 12). Using (1)/(v) - (1)/(u) = (1)/(f) with u = −(2f − 12), v = +3(2f − 12): (1)/(3(2f-12)) + (1)/(2f-12) = (1)/(f) ⇒ (4)/(3(2f-12)) = (1)/(f) 4f = 6f - 36 ⇒ f = 18 cm. Focal length = 18 cm.