LensesClass 10 Science Part 1 Chapter 7 Notes – Maharashtra Board

Summary: Lenses

A lens is a piece of transparent material with two curved surfaces, or one curved and one flat surface. A convex lens is fat in the middle and brings parallel rays together at a point. A concave lens is thin in the middle and spreads parallel rays apart. Light bends twice in a lens, once when it enters and once when it leaves.

Using just a few simple rays, we can draw where an image will form, how big it is, and whether it is real or virtual. A convex lens can make real, inverted images of many sizes, and a magnified upright image when the object is very close. A concave lens always gives a small, upright, virtual image.

The lens formula 1/v − 1/u = 1/f connects the object distance, image distance and focal length, provided we follow the Cartesian sign convention carefully. Magnification tells us how big the image is, and power, measured in dioptres, tells us how strongly a lens bends light. Powers of lenses in contact simply add up.

Our eye is a living camera. Its convex lens changes shape with the help of ciliary muscles so that both far and near objects form sharp images on the retina. When this ability fails we get myopia, hypermetropia or presbyopia, which are corrected with concave, convex or bifocal spectacles.

Lenses are everywhere: in door peepholes, torches, cameras, microscopes and telescopes. The chapter also explains why a moving incense stick seems to draw a glowing circle (persistence of vision) and why we see colours only in bright light (cone cells in the retina).

Key points to remember

• A convex lens is thicker at the centre and converges light; a concave lens is thinner at the centre and diverges light.
• A ray passing through the optical centre of a lens goes straight without bending.
• Focal length (f) is the distance between the optical centre and the principal focus.
• For a convex lens, an object at 2F₁ gives a real, inverted, same-size image at 2F₂.
• An object placed between F₁ and O of a convex lens gives a virtual, erect and enlarged image on the same side.
• A concave lens always forms a virtual, erect and diminished image between O and F₁.
• Lens formula: 1/v − 1/u = 1/f; the object distance u is always negative in the Cartesian sign convention.
• Focal length of a convex lens is positive and of a concave lens is negative.
• Magnification M = h₂/h₁ = v/u; a negative M means a real, inverted image.
• Power P = 1/f (f in metre); unit is dioptre (D). For lenses in contact, P = P₁ + P₂.
• The near point of a normal eye is 25 cm and the far point is at infinity.
• Myopia is corrected by a concave lens (negative power); hypermetropia by a convex lens (positive power).
• Presbyopia is age-related loss of accommodation; bifocal lenses help people who have both defects.
• The impression of an image stays on the retina for about 1/16th of a second — persistence of vision.

Lenses – Notes

1. Lenses and their types

• A lens is a transparent medium bounded by two surfaces, at least one of which is usually spherical.
• A convex (double convex) lens bulges outwards on both sides, so it is thicker in the middle than at the edges.
• A concave (double concave) lens is curved inwards on both sides, so it is thinner in the middle than at the edges.
• Other shapes include plano-convex, plano-concave, positive meniscus and negative meniscus lenses.
• A ray of light is refracted twice in a lens — on entering and on leaving — and this changes its direction.
• Everyday examples: reading glasses of grandparents, the peephole in a flat's main door, and the eyepiece a watch repairer fixes to his eye.

2. Terms related to a lens

• Centre of curvature (C): the centre of the sphere of which a lens surface is a part. A lens with two curved surfaces has two centres, C₁ and C₂.
• Radius of curvature (R): the radius of that sphere; the two surfaces have radii R₁ and R₂.
• Principal axis: the imaginary straight line joining the two centres of curvature.
• Optical centre (O): the point on the principal axis inside the lens through which light passes without changing direction.
• Principal focus (F): for a convex lens, the point where rays parallel to the axis actually meet after refraction; for a concave lens, the point from which such rays appear to spread out. Every lens has two foci, F₁ and F₂.
• Focal length (f): distance from O to F. A convex lens is called a converging lens and a concave lens a diverging lens.
• Quick way to find f of a convex lens: focus the image of a far-away tree on a wall and measure the lens-to-wall distance.

3. Ray diagrams and images formed by a convex lens

• Rule 1: a ray parallel to the principal axis passes through the principal focus F₂ after refraction.
• Rule 2: a ray passing through the focus F₁ becomes parallel to the principal axis after refraction.
• Rule 3: a ray through the optical centre O goes straight on without changing direction.
• Any two of these rays are enough; where they meet (or appear to meet) is the image of the top of the object.
• Object at infinity → point image at F₂, real and inverted. Beyond 2F₁ → between F₂ and 2F₂, smaller, real, inverted. At 2F₁ → at 2F₂, same size, real, inverted.
• Between F₁ and 2F₁ → beyond 2F₂, larger, real, inverted. At F₁ → at infinity, very large, real, inverted.
• Between F₁ and O → on the same side as the object, enlarged, virtual and erect. This is how a magnifying glass works.
• A real image can be caught on a screen; a virtual image cannot, it can only be seen by looking through the lens.

4. Images formed by a concave lens

• Rule 1: a ray parallel to the principal axis, after refraction, appears to come from the focus F₁ when extended backwards.
• Rule 2: a ray aimed towards the focus on the far side becomes parallel to the principal axis after refraction.
• A ray through the optical centre goes undeviated, as in any lens.
• Object at infinity → point image at F₁, virtual and erect.
• Object anywhere between O and infinity → image between O and F₁, diminished, virtual and erect.
• So a concave lens can never form a real or magnified image of a real object — the reason a door peephole shows a small, wide view of the corridor.

5. Sign convention, lens formula and magnification

• In the Cartesian sign convention the optical centre O is the origin and the principal axis is the x-axis.
• The object is always kept on the left of the lens, so the object distance u is always negative.
• Distances measured to the right of O are positive; those to the left are negative.
• Heights above the principal axis are positive; heights below it are negative.
• Focal length of a convex lens is positive; focal length of a concave lens is negative.
• The lens formula 1/v − 1/u = 1/f holds for every spherical lens and every object position — only the signs change.
• Magnification M = h₂/h₁ = v/u. Negative M means the image is real and inverted; positive M means virtual and erect. |M| > 1 means enlarged.

6. Power of a lens and combination of lenses

• Power (P) is the ability of a lens to converge or diverge light. A shorter focal length means a stronger lens and greater power.
• P = 1/f, where f must be in metres. The SI unit is the dioptre (D); 1 D is the power of a lens of focal length 1 m.
• A convex lens has positive power; a concave lens has negative power. An optician's prescription of −2.0 D means a concave lens.
• When two thin lenses touch each other, 1/f = 1/f₁ + 1/f₂, i.e. P = P₁ + P₂.
• Activity link: a lens of shorter focal length burns paper faster in sunlight because it brings light to a sharper, closer focus.

7. Human eye and power of accommodation

• Cornea: thin transparent front membrane; most of the bending of light happens at its outer surface.
• Iris: dark muscular screen behind the cornea that gives the eye its colour. Pupil: the hole in the iris that becomes small in bright light and wide in dim light, controlling how much light enters.
• Eye lens: a double convex, transparent, flexible lens behind the pupil; it forms a real, inverted image on the retina, a screen of light-sensitive cells.
• Retina cells produce electrical signals that travel through the optic nerve to the brain, which lets us see the object upright and as it really is.
• Ciliary muscles change the lens shape: for far objects the lens becomes flatter (focal length increases); for near objects it becomes more rounded (focal length decreases).
• Power of accommodation is this ability of the eye lens to change its focal length as needed — but only within a limit.
• Normal eye: near point (least distance of distinct vision) = 25 cm; far point = infinity. The eyeball is about 2.4 cm across and the relaxed eye has a focal length of about 2 cm.
• Apparent size depends on the angle the object makes at the eye: a nearer object makes a bigger angle and looks bigger, which is why we bring small things close — but not closer than 25 cm.

8. Defects of vision and their correction

• Myopia (nearsightedness): near objects are clear but distant ones are blurred; the far point comes closer and the image of a far object forms in front of the retina.
• Causes of myopia: the cornea and lens become too curved (too much converging power), or the eyeball becomes longer. Correction: a concave lens of suitable negative power.
• Hypermetropia (farsightedness): distant objects are clear but near ones are blurred; the near point moves beyond 25 cm and the image forms behind the retina.
• Causes of hypermetropia: the cornea and lens become less curved (less converging power), or the eyeball becomes shorter. Correction: a convex lens of suitable positive power.
• Presbyopia: with age the ciliary muscles weaken and the lens loses flexibility, so the near point moves away — many grandparents hold the newspaper at arm's length.
• A person with both near and far defects uses bifocal lenses: concave in the upper part (for distance) and convex in the lower part (for reading).

9. Uses of lenses

• Concave lenses: laser-based devices such as CD players, scanners and medical instruments; door peepholes; spectacles for myopia; torches (to spread the beam); and with convex lenses in cameras, microscopes and telescopes to improve image quality.
• Simple microscope (magnifying glass): a convex lens of short focal length with the object between F and O gives a virtual, erect, enlarged image — up to about 20 times. Used by watch repairers and jewellers checking gems.
• Compound microscope: two convex lenses — an objective (small aperture, short focal length) and an eyepiece (bigger, longer focal length). The image by the objective acts as the object for the eyepiece, so magnification happens in two stages. Used to see cells and bacteria.
• Telescope: for viewing distant objects. Refracting telescopes use lenses; reflecting telescopes use mirrors and lenses.
• In a telescope the objective has a large diameter and long focal length to collect plenty of light; the eyepiece is smaller with shorter focal length. Changing the eyepiece changes the magnification.
• Convex lenses are also used in cameras, projectors, spectrographs and spectacles for hypermetropia.

10. Persistence of vision and colour vision

• The image of an object does not vanish from the retina the instant the object is removed; it stays for about 1/16th of a second. This is persistence of vision.
• That is why a whirled incense stick looks like a glowing ring, and why a spinning card with a bird on one side and a cage on the other shows the bird inside the cage. Cinema and cartoons work the same way.
• The retina has two kinds of light-sensitive cells: rod cells and cone cells.
• Rod cells respond to the intensity of light (bright or dim) and work even in faint light.
• Cone cells respond to colour (red, green and blue) but need bright light, so we cannot make out colours in dim light.
• People who lack cone cells for certain colours cannot tell those colours apart; they are colour blind, though their eyesight is otherwise normal.

Formulas at a glance

Key terms

Lenses – Flashcards

Read the question, answer it in your head, then tap the card to check. 20 cards.

Lenses – MCQ Quiz

15 questions. Tap an option — you will see at once if it is right and why.

How to study Lenses

⏱ About 4 hours over 3 days

1. Day 1 — Lens basics and ray diagrams
   Read the notes on types of lenses and lens terms. Draw a convex and a concave lens and label C₁, C₂, O, F₁, F₂ and f. Learn the three ray rules, then draw all six convex-lens ray diagrams and the concave-lens diagram from memory. Make your own table of object position vs image position, size and nature.
2. Day 2 — Sign convention, lens formula, power
   Write the five sign-convention rules on a card. Work through both solved examples in these notes without looking, then make up three numericals of your own (change u and f) and solve them. Practise power and combination problems, always converting cm to m before using P = 1/f.
3. Day 3 — Eye, defects and uses
   Draw and label the human eye. Make a two-column comparison of myopia and hypermetropia (symptom, image position, causes, correcting lens, sign of power) and draw their correction diagrams. Revise uses of lenses, persistence of vision and rods and cones. Finish with our flashcards and the 15-question quiz; re-read any section where you made a mistake.

✍️ Diagrams to practise

• Labelled convex and concave lens showing C₁, C₂, principal axis, O, F₁, F₂ and focal length
• Ray diagrams for a convex lens for all six object positions
• Ray diagram for the image formed by a concave lens
• Cartesian sign convention diagram for lenses
• Labelled structure of the human eye
• Myopic and hypermetropic eye with their correction by concave and convex lenses
• Simple microscope, compound microscope and refracting telescope (ray sketches)