Lenses Class 10 Notes, Formulas, Questions | SSC

This chapter studies lenses, transparent media bounded by two surfaces, and how they form images by refraction. It defines the terms used for lenses, gives the rules for ray diagrams and the images formed by convex and concave lenses, and introduces the Cartesian sign convention, lens formula, magnification and power. It then explains the structure and working of the human eye, defects of vision and their correction, and uses of lenses in microscopes, telescopes and other devices.

Summary

A lens is a transparent medium bound by two surfaces, usually parts of spheres. A convex (double convex) lens bulges outwards and is thicker at the centre than at the edges; a concave (double concave) lens is curved inwards and is thinner at the centre. A ray passing through a lens is refracted twice, once on entering and once on leaving, and its direction changes.

Important terms: the centres of the spheres forming the lens surfaces are the centres of curvature (C1, C2) and their radii are the radii of curvature (R1, R2). The line through both centres of curvature is the principal axis. The optical centre O is the point on the principal axis inside the lens through which rays pass without changing direction. Rays parallel to the principal axis converge to a point (principal focus) after passing through a convex lens, so it is a converging lens; for a concave lens they diverge and appear to come from the principal focus, so it is a diverging lens. The distance from the optical centre to the principal focus is the focal length f.

Ray diagrams for a convex lens use three rules: a ray parallel to the principal axis passes through the principal focus after refraction; a ray through the principal focus becomes parallel to the principal axis; a ray through the optical centre goes straight. With the object at infinity, beyond 2F1, at 2F1 or between F1 and 2F1, the image is real and inverted (point size at F2; smaller between F2 and 2F2; same size at 2F2; larger beyond 2F2). With the object at F1 the image is at infinity, very large, real and inverted. With the object between F1 and O, the image is virtual, erect and enlarged on the same side as the object. A concave lens always forms a virtual, erect and smaller image between the optical centre and the focus F1 (a point image at F1 for an object at infinity).

According to the Cartesian sign convention, the optical centre is the origin and the principal axis is the X-axis. The object is kept on the left of the lens and all distances are measured from O; distances to the right of O are positive and to the left are negative; heights above the axis are positive and below are negative. The focal length of a convex lens is positive and that of a concave lens is negative. Using this convention, the lens formula 1/v - 1/u = 1/f relates object distance u, image distance v and focal length f for every spherical lens. Magnification M is the ratio of image height to object height, h2/h1, and also equals v/u; a negative M means a real, inverted image.

The power of a lens is its ability to converge or diverge rays and equals the reciprocal of its focal length in metres; its unit is the dioptre (D), where 1 D = 1 per metre. A convex lens has positive power and a concave lens negative power. For lenses kept in contact, 1/f = 1/f1 + 1/f2 and the total power is P = P1 + P2.

In the human eye, light enters through the transparent cornea, where most refraction takes place. The iris is a dark, fleshy screen whose central opening, the pupil, controls the amount of light entering: it contracts in bright light and widens in dim light. Behind the pupil is a double convex crystalline lens that forms a real, inverted image on the retina, whose light-sensitive cells send electrical signals to the brain through the optic nerve. The ciliary muscles change the shape of the lens: it becomes flatter with a longer focal length for distant objects and more rounded with a shorter focal length for near objects. This ability is called the power of accommodation. The eyeball is about 2.4 cm in diameter and the relaxed focal length is about 2 cm. For a normal eye the near point is at 25 cm and the far point is at infinity.

Defects of vision arise when accommodation fails. In nearsightedness (myopia), distant objects look blurred because the image forms in front of the retina, due to increased curvature of the cornea and lens or an elongated eyeball; it is corrected by a concave lens of suitable negative power. In farsightedness (hypermetropia), near objects look blurred because the image forms behind the retina, due to decreased curvature or a flattened eyeball; it is corrected by a convex lens of positive power. Presbyopia is the loss of focusing power with age, which shifts the near point away; people with both defects use bifocal lenses with a concave upper part and a convex lower part. The apparent size of an object depends on the angle it subtends at the eye.

Concave lenses are used in laser instruments such as scanners and CD players, door peep holes, spectacles for myopia and torches; camera, telescope and microscope mainly use convex lenses. A simple microscope is a convex lens of short focal length that gives a virtual, erect, enlarged image (up to about 20 times), used by watch repairers and to test gems. A compound microscope uses two convex lenses, a small objective of short focal length and a larger eyepiece, giving magnification in two stages. Telescopes may be refracting (lenses) or reflecting (mirrors and lenses); the objective has a large diameter and long focal length. The image stays on the retina for about 1/16 of a second after the object is removed (persistence of vision). Rod cells respond to light intensity and cone cells to colour; cones do not work in faint light, and people lacking some cone cells are colour blind.

Mind map

Solving a lens numerical step by step

Important definitions

Formulas

Key points to remember

• A convex lens is a converging lens; a concave lens is a diverging lens.
• A ray through the optical centre goes undeviated; a ray parallel to the axis passes through (or appears to come from) the focus.
• Convex lens: object at 2F1 gives a real, inverted image of the same size at 2F2.
• Convex lens: object between F1 and O gives a virtual, erect, enlarged image on the same side; this is how a magnifying glass works.
• A concave lens always gives a virtual, erect, diminished image between O and F1.
• Sign convention: u is always negative for a real object; f is positive for convex and negative for concave lenses.
• Negative magnification means real and inverted image; positive magnification means virtual and erect image.
• Power P = 1/f with f in metres; unit dioptre (D).
• Normal eye: near point 25 cm, far point at infinity; eyeball diameter about 2.4 cm.
• Myopia is corrected by a concave lens, hypermetropia by a convex lens, and both together by bifocal lenses.
• Rod cells sense brightness; cone cells sense colour and work only in bright light.

Solved examples

Example 1. An object 5 cm high is placed 20 cm from a convex lens of focal length 10 cm. Find the position, size and nature of the image.

Given: h1 = 5 cm, f = +10 cm, u = -20 cm.

1/v = 1/f + 1/u = 1/10 + 1/(-20) = 1/10 - 1/20 = 1/20, so v = +20 cm.

M = v/u = 20 / (-20) = -1.

h2 = M x h1 = -1 x 5 = -5 cm.

The image is 20 cm on the other side of the lens, real, inverted and of the same size as the object (object is at 2F1, image at 2F2).

Example 2. The focal length of a convex lens is 20 cm. What is its power?

f = 20 cm = 0.2 m.

P = 1/f = 1/0.2 = 5 D.

The power of the lens is +5 D.

Example 3. A doctor prescribes a lens of power +1.5 D. Find its focal length. Which lens is it and which defect does it correct?

f = 1/P = 1/1.5 = 0.67 m (approximately).

Since power and focal length are positive, it is a convex lens. A convex lens is used to correct farsightedness (hypermetropia).

Example 4. A 5 cm high object is placed 25 cm from a converging lens of focal length 10 cm. Find the position, size and type of image.

Given: h1 = 5 cm, u = -25 cm, f = +10 cm.

1/v = 1/f + 1/u = 1/10 - 1/25 = (5 - 2)/50 = 3/50, so v = 50/3 = 16.7 cm.

M = v/u = 16.7 / (-25) = -0.67.

h2 = M x h1 = -0.67 x 5 = -3.3 cm.

The image is 16.7 cm behind the lens, 3.3 cm tall, real, inverted and smaller.

Example 5. Three lenses of power 2 D, 2.5 D and 1.7 D are kept touching in a row. What is their total power?

For lenses in contact, P = P1 + P2 + P3 = 2 + 2.5 + 1.7 = 6.2 D.

Example 6. An object kept 60 cm from a lens gives a virtual image 20 cm in front of the lens. Find the focal length. Is the lens converging or diverging?

The object and the virtual image are both on the left: u = -60 cm, v = -20 cm.

1/f = 1/v - 1/u = -1/20 + 1/60 = (-3 + 1)/60 = -2/60 = -1/30.

f = -30 cm.

The negative focal length shows it is a diverging (concave) lens.

Example 7. An object is placed 30 cm in front of a concave lens of focal length 15 cm. Find the image position and magnification.

u = -30 cm, f = -15 cm.

1/v = 1/f + 1/u = -1/15 - 1/30 = (-2 - 1)/30 = -3/30, so v = -10 cm.

M = v/u = (-10)/(-30) = +1/3.

The image is 10 cm from the lens on the object side, virtual, erect and one-third the size of the object.

Important questions and answers

Q1. Where should an object be kept in front of a convex lens to get a real image of the same size as the object?

At 2F1 (twice the focal length from the lens). The image is formed at 2F2 on the other side; it is real, inverted and of the same size.

Q2. Give reason: A simple microscope is used for watch repairs.

A simple microscope is a convex lens of short focal length. When the tiny parts of a watch are kept between its focus and optical centre, it forms a virtual, erect and enlarged image, so small parts can be seen clearly while repairing.

Q3. Give reason: We can sense colours only in bright light.

Colour is detected by the cone cells of the retina. Cone cells do not respond to faint light; only rod cells, which sense brightness, work in dim light. So colours can be perceived only in bright light.

Q4. Give reason: We cannot clearly see an object kept at a distance less than 25 cm from the eye.

The near point of a normal eye is 25 cm. For closer objects the eye lens cannot decrease its focal length any further (its accommodation has a limit), so the image cannot be focused on the retina and the object looks blurred.

Q5. Distinguish between nearsightedness and farsightedness.

Nearsightedness (myopia): near objects are clear but distant ones are blurred; far point comes closer than infinity; image of distant objects forms in front of the retina; caused by increased curvature of cornea and lens or an elongated eyeball; corrected by a concave lens (negative power).

Farsightedness (hypermetropia): distant objects are clear but near ones are blurred; near point moves beyond 25 cm; image of near objects forms behind the retina; caused by decreased curvature or a flattened eyeball; corrected by a convex lens (positive power).

Q6. Distinguish between a convex lens and a concave lens.

Convex lens: thicker at the centre, converging, positive focal length and power, forms real or virtual images depending on object position, used for hypermetropia and in microscopes.

Concave lens: thinner at the centre, diverging, negative focal length and power, always forms virtual, erect, diminished images, used for myopia, peep holes and torches.

Q7. What is the function of the iris and the muscles connected to the lens in the human eye?

The iris is a dark muscular screen that adjusts the size of the pupil: the pupil contracts in bright light and widens in dim light, controlling the amount of light entering the eye. The ciliary muscles change the curvature of the eye lens, making it flatter for distant objects and more rounded for near objects, so the image is always focused on the retina (accommodation).

Q8. State the Cartesian sign convention for lenses.

1. The object is always placed to the left of the lens and all distances are measured from the optical centre.

2. Distances to the right of O are positive, to the left are negative.

3. Heights above the principal axis are positive; heights below are negative.

4. Focal length of a convex lens is positive and of a concave lens is negative.

Q9. What is presbyopia? How is it corrected?

With age, the muscles near the eye lens lose their ability to change its focal length, so the near point shifts away and nearby objects cannot be seen clearly. This is presbyopia. If a person has both near and far vision problems, bifocal lenses are used: the upper part is concave for distant vision and the lower part is convex for reading.

Q10. Explain the working of a compound microscope.

It has two convex lenses fixed in a metal tube on the same axis: an objective of small aperture and short focal length, and an eyepiece of larger aperture and longer focal length. The objective forms a magnified image of the tiny object; this image acts as the object for the eyepiece, which magnifies it further. Thus magnification occurs in two stages, allowing cells and bacteria to be observed.

Q11. What is persistence of vision? Give an example.

The image of an object remains on the retina for about 1/16 of a second after the object is removed; this is persistence of vision. Example: a burning incense stick rotated fast appears as a glowing circle, and a card with a cage on one side and a bird on the other, spun fast, shows the bird inside the cage.

Exam tips

• Learn the convex lens image table (six object positions) thoroughly; it is asked as diagrams, tables and MCQs.
• In every numerical write the sign convention values before substituting; most mistakes come from the sign of u.
• Convert focal length to metres before calculating power.
• Draw ray diagrams with arrows on rays, dotted lines for virtual rays, and label F1, 2F1, F2, 2F2 and O.
• For eye defects, always state the cause, where the image forms and the correcting lens.

FAQs

Why is the focal length of a concave lens negative?

Its principal focus lies on the same side as the object (to the left of the optical centre), and by the Cartesian sign convention distances to the left are negative.

What does a negative magnification mean?

It means the image is inverted and real, formed below the principal axis. A positive magnification means a virtual, erect image.

How does the eye see near and far objects clearly?

The ciliary muscles change the shape of the eye lens: it becomes flatter (longer focal length) for distant objects and more rounded (shorter focal length) for near objects. This is accommodation.

What is the unit of power of a lens?

The dioptre (D). One dioptre is the power of a lens whose focal length is 1 metre.

These notes were prepared with AI help from the Balbharati Science and Technology Part 1 textbook (2026-27) and checked against it.