Class 10 Science Chapter 9 — Light: Reflection and Refraction (International Edition)
NCERT / RBSE Syllabus 2026–27 · Learn by doing · Includes three labelled diagrams
Prepared by: NCERTClasses Team — textbook specialists and experienced teachers.
Based on: NCERT Class 10 Science textbook, Chapter 9, and the Board of Secondary Education, Rajasthan syllabus 2026–27.
Published: 24 September 2026 · Last updated: 24 September 2026
Look into the inside of a shiny spoon, close up — your face appears upright and magnified. Move it further away and, at some point, your face flips upside down. Now turn the same spoon around and look at its outer curve — your face stays upright, always, just smaller. Same spoon, and the image changes with distance — why?
And why does a pencil in a glass of water appear bent at the surface, when the pencil itself is perfectly straight?
- Concave mirror (curves inward) — converging, image depends on object position. Convex mirror (curves outward) — diverging, always small-upright-virtual image.
- Mirror formula: 1/v + 1/u = 1/f · Magnification: m = −v/u = h'/h
- New Cartesian Sign Convention — measure distances from the pole; positive in the direction of incident light, negative opposite to it.
- Refraction — light bends when it changes medium, because its speed changes. Refractive index n quantifies exactly this.
- Convex lens (thick middle) — converging. Concave lens (thin middle) — diverging.
- Lens formula: 1/v − 1/u = 1/f · Power: P = 1/f (f in metres), unit dioptre (D).
How to read this — first you think or try it, then comes the explanation:
🔍 Wonder · 🧪 Try it · 📖 Understand · 🔗 Apply · ✅ Check yourself
"Check yourself" has three levels — 1, 2, 3.
Contents
- Foundation check
- Spherical mirrors — types and images
- How to construct ray diagrams
- Sign convention
- Mirror formula and magnification
- Refraction — why direction changes
- Refractive index
- Spherical lenses — types and images
- Lens formula, magnification and power
- Your ladder
- Marking scheme
- Common mistakes
- Final test
- Glossary
- For parents and teachers
- Beyond NCERT
Foundation check
- What is the law of reflection? (Class 8–9)
- What kind of image does a plane mirror form?
- What is focal length?
Answers
1. Angle of incidence = angle of reflection, and the incident ray, reflected ray and normal all lie in the same plane. 2. Virtual, upright, same size as the object, as far behind the mirror as the object is in front. 3. The distance from the pole to the principal focus. This chapter applies these same ideas to curved surfaces — mirrors and lenses.
1. Spherical mirrors — types and images
🔍 Wonder — A doctor's head mirror, a car's side mirror, and the reflector behind a torch bulb are all spherical mirrors — so why does each do such a different job?
🧪 Try it — Take a shiny steel bowl. Bring your finger close to its inner surface, then slowly move it away. Think first — will the image always look the same, or change with distance?
What happened? Very close, your finger appeared large and upright; further away, it flipped upside down — and somewhere in between, it likely blurred out entirely. That is the defining trait of a concave mirror — the image depends entirely on how far the object is.
Figure 1 — For an object beyond the centre of curvature (C), a concave mirror forms a real, inverted, diminished image between C and the principal focus (F).
📖 Understand — A mirror that curves inward (bowl-shaped) is called a concave mirror — it is converging, meaning it brings parallel rays together at a single point, the principal focus. A mirror that curves outward is a convex mirror — it is diverging.
| Object position (concave mirror) | Image |
|---|---|
| At infinity | At F, point-sized, real, highly diminished |
| Beyond C | Between C and F, real, inverted, diminished |
| Exactly at C | Exactly at C, real, inverted, same size |
| Between C and F | Beyond C, real, inverted, enlarged |
| Exactly at F | At infinity, real, highly enlarged |
| Between F and pole (P) | Behind the mirror, virtual, upright, enlarged |
A convex mirror is always simple — wherever the object is, the image is always virtual, upright and smaller, behind the mirror. This is exactly why it is used in vehicle side mirrors — it gives a wider field of view.
🔗 Apply — Back to the opening question: the bowl's inner surface is concave — held close (within F), it gave a virtual, magnified image; moved further (beyond F), it gave a real, inverted image. A doctor's head mirror is concave too — for exactly this reason, giving a magnified image of whatever is examined close up.
✅ Check yourself
Level 1 Which mirror is converging? — Answer: The concave mirror.
Level 2 Why are convex mirrors fitted to vehicles? — Answer: They always give a virtual, upright, smaller image, letting a much larger area behind the vehicle be seen at once — a wider field of view.
Level 3 If an object sits exactly at the focus (F) of a concave mirror, where does the image form, and why is this a practically awkward case? — Answer: The image forms at infinity, greatly enlarged. This is awkward because the reflected rays become nearly parallel to each other and never truly meet — practically, a sharp, finite image is hard to pin down. This exact principle is used in reverse in torches and searchlights — placing the bulb at F produces a parallel beam of light.
2. How to construct ray diagrams
📖 Understand — To find the exact position of an image, you need at least two rays whose reflected path is already known:
| Ray | Rule |
|---|---|
| Parallel to the principal axis | After reflection (concave), passes through the principal focus — or (convex), appears to come from the focus |
| Passing through the principal focus | After reflection, becomes parallel to the principal axis |
| Passing through the centre of curvature (C) | Reflects straight back along the same path (it strikes the mirror along the normal) |
| Striking the pole (P) | Reflects following the law of reflection (equal angles to the principal axis) |
🔗 Apply — Draw any two of these rays; the point where they cross is the top of the image.
3. Sign convention
📖 Understand — To get correct results from the formulas, the New Cartesian Sign Convention is used:
- All distances are measured from the pole (P).
- The object is always placed to the left of the mirror — light travels left to right.
- Distances measured in the direction light travels are positive (+); against it, negative (−).
- Heights measured above the principal axis are positive; below, negative.
This has a direct consequence: object distance (u) is always negative (the object sits to the left). A concave mirror's focal length is negative; a convex mirror's is positive.
✅ Check yourself
Level 1 What sign does object distance (u) always take? — Answer: Negative.
Level 2 What sign does a concave mirror's focal length take, and why? — Answer: Negative — because its focus sits in front of the mirror, to the left, opposite to the direction light travels.
4. Mirror formula and magnification
📖 Understand — The relationship between object distance (u), image distance (v) and focal length (f):
1/v + 1/u = 1/f
Magnification tells you how much bigger/smaller and upright/inverted the image is compared to the object:
m = h'/h = −v/u
where h' is image height, h is object height. Positive m means the image is upright (and virtual); negative m means inverted (and real).
Worked example 1: A concave mirror has a focal length of 15 cm. Where does it form the image of an object placed 30 cm away?
Solution: f = −15 cm, u = −30 cm. Substituting: 1/v = 1/f − 1/u = (1/−15) − (1/−30) = −1/15 + 1/30 = −1/30. So v = −30 cm — the image also forms at 30 cm, real (v is negative). The object was exactly at the centre of curvature (C = 2f = 30 cm), so the image forms there too, matching the table above — same size as the object.
Worked example 2: An object 2 cm tall is placed 10 cm from a concave mirror of focal length 15 cm. Find the image position and height.
Solution: f = −15, u = −10. 1/v = 1/f − 1/u = (1/−15) − (1/−10) = −1/15 + 1/10 = 1/30. So v = +30 cm — positive, meaning the image is virtual, behind the mirror. Magnification: m = −v/u = −(30)/(−10) = +3. Image height h' = m × h = 3 × 2 = 6 cm, upright (positive m) — this matches the table: object between F and P gives a virtual, upright, enlarged image.
✅ Check yourself
Level 1 What is the formula for magnification? — Answer: m = h'/h = −v/u.
Level 2 If m = +2 is obtained, what kind of image is it? — Answer: Upright, virtual, twice the size of the object.
Level 3 Find the image position for an object placed 40 cm from a convex mirror of focal length +20 cm. — Answer: u = −40, f = +20. 1/v = 1/f − 1/u = 1/20 − (−1/40) = 1/20 + 1/40 = 3/40. v = 40/3 ≈ +13.3 cm — positive, meaning behind the mirror, virtual — exactly as always expected from a convex mirror.
5. Refraction — why direction changes
🔍 Wonder — Why does a pencil dipped in water look bent?
🧪 Try it — Put a pencil tilted into a glass of water and view it from the side. Think first — does the pencil actually bend, or is it a trick of the eye?
📖 Understand — When light enters one medium (air) from another (water or glass) at an angle, its speed changes, and because of that its direction bends — this is called refraction. The pencil doesn't really bend — the rays travelling from the underwater part to your eye bend, so your brain perceives them as coming from the wrong place.
Figure 2 — Entering glass from air, the ray bends toward the normal; leaving the glass, it bends back by an equal angle, becoming parallel to its original direction, but laterally displaced.
🔗 Apply — Notice: the emergent ray is parallel to the original incident ray — just shifted sideways. This happens because the slab's two surfaces are parallel to each other.
✅ Check yourself
Level 1 What causes refraction? — Answer: A change in the speed of light when it changes medium.
Level 2 How does the emergent ray from a rectangular slab relate to the original incident ray? — Answer: It is parallel to it, just laterally displaced.
6. Refractive index
📖 Understand — Every medium lets light pass at a different speed. A medium's refractive index (n) tells you how much slower light travels in it compared to vacuum/air:
n = speed of light in vacuum (c) / speed of light in the medium (v)
The higher the refractive index, the denser the medium optically, and the more the ray bends. Diamond's refractive index is far higher than water's — which is exactly why light bends so dramatically inside diamond, giving it its famous sparkle.
✅ Check yourself
Level 1 What does a higher refractive index mean? — Answer: Light travels slower in that medium, which is optically denser.
7. Spherical lenses — types and images
🔍 Wonder — Why does a magnifying glass make small things look bigger, while a pair of spectacles can make the very same object look smaller?
🧪 Try it — If a magnifying glass or spectacle lens is at hand, use it to look at printed text, moving it closer and further away. Think first — does the lens's shape (thick or thin in the middle) have anything to do with it?
Figure 3 — For an object beyond 2F1, a convex lens forms a real, inverted, diminished image between F2 and 2F2.
📖 Understand — A lens that is thick in the middle, thin at the edges is a convex lens — converging. One that is thin in the middle, thick at the edges is a concave lens — diverging.
| Object position (convex lens) | Image |
|---|---|
| At infinity | At F2, real, highly diminished |
| Beyond 2F1 | Between F2 and 2F2, real, inverted, diminished |
| Exactly at 2F1 | Exactly at 2F2, real, inverted, same size |
| Between F1 and 2F1 | Beyond 2F2, real, inverted, enlarged |
| Exactly at F1 | At infinity, real, highly enlarged |
| Between F1 and optical centre (O) | Same side as the object, virtual, upright, enlarged — the magnifying-glass case |
A concave lens is always simple — wherever the object is, the image is always virtual, upright and smaller, on the same side as the object.
🔗 Apply — Back to the opening question: a magnifying glass places the object within F1 — that's the only way to get an enlarged, virtual image. Spectacle lenses serve a different goal entirely — not magnifying the world, but correcting where the eye's own image lands (on the retina), so depending on the defect, glasses may use either convex or concave lenses.
✅ Check yourself
Level 1 Which lens always gives a smaller, virtual image? — Answer: The concave lens.
Level 2 Where must the object sit to use a convex lens as a magnifying glass? — Answer: Between the principal focus (F1) and the optical centre.
Level 3 Will two convex lenses placed together always behave exactly like one bigger convex lens? — Answer: Generally the combined focal length will change (powers add, covered below), but the exact behaviour depends on both lenses' focal lengths and the distance between them — this precise combination is beyond Class 10 NCERT level.
8. Lens formula, magnification and power
📖 Understand — The same sign convention applies to lenses (distances from the optical centre, positive in the direction light travels). But the lens formula differs slightly from the mirror formula:
1/v − 1/u = 1/f
Magnification: m = h'/h = v/u (no negative sign here, unlike the mirror formula)
A lens's power tells you how strongly it bends/converges light:
P = 1/f (f in metres)
Unit: dioptre (D). A convex lens has positive power, a concave lens negative. The shorter the focal length, the higher the power — the stronger the bending ability.
Worked example 3: A convex lens has a focal length of 25 cm. Find its power.
Solution: f = 25 cm = 0.25 m. P = 1/f = 1/0.25 = +4 D.
Worked example 4: An object 3 cm tall is placed 20 cm from a convex lens of focal length 10 cm. Find the image position, magnification and height.
Solution: f = 10, u = −20. 1/v = 1/f + 1/u = 1/10 + (−1/20) = 1/20. So v = +20 cm — real image, formed on the far side. Magnification: m = v/u = 20/(−20) = −1. Image height = m × h = −1 × 3 = −3 cm — same size as the object, inverted (negative). This matches the table: object exactly at 2F1 gives a same-size, inverted image at 2F2.
🔗 Apply — When a doctor prescribes glasses with power "+2" or "−1.5", that number is the lens power in dioptres — positive means a convex lens (for long-sightedness), negative means a concave lens (for short-sightedness).
✅ Check yourself
Level 1 What is the unit of lens power? — Answer: Dioptre (D).
Level 2 What is the power of a lens with focal length −25 cm, and what kind of lens is it? — Answer: P = 1/(−0.25) = −4 D — negative power, a concave lens.
Level 3 What is the focal length of a lens with power +2 D? — Answer: f = 1/P = 1/2 = 0.5 m = 50 cm — positive, so a convex lens with a focal length of 50 cm.
Your ladder
| Level | Total | If you got this many right | You are |
|---|---|---|---|
| Level 1 | 10 | 8+ | Familiar |
| Level 2 | 10 | 7+ | Proficient — board-exam ready |
| Level 3 | 5 | 4+ | Skilled |
Marking scheme
(An example of a typical examiner's approach — not an official scheme.)
Question (5 marks): An object is placed 30 cm from a convex lens of focal length 20 cm. Find the image position, nature and magnification, and draw the ray diagram.
Correct substitution into the formula (right sign for u, f). 1 mark
Correct calculation of v. 1 mark
Magnification and correctly stating the image's nature. 1 mark
Correctly labelled ray diagram. 2 marks
Common mistakes
| Common mistake | Correct fact |
|---|---|
| "A concave mirror always gives a bigger image" | Depends on object position — beyond C, the image can be smaller too. |
| "Taking object distance (u) as positive" | In the New Cartesian convention, u is always negative (object is to the left). |
| "The mirror and lens formulas are the same" | Mirror: 1/v + 1/u = 1/f. Lens: 1/v − 1/u = 1/f — the sign differs. |
| "A higher refractive index means faster light" | The opposite — a higher refractive index means light travels slower in that medium. |
| "A convex lens never gives a smaller image" | It does — when the object is beyond 2F1, the image is smaller than the object. |
Final test — mixed
8+ correct = chapter mastered.
- Which mirror always gives a virtual, smaller image?
- State the mirror formula.
- In the New Cartesian convention, what sign does object distance take?
- What is the main cause of refraction?
- What does a higher refractive index mean?
- Which lens is diverging?
- State the lens formula.
- What is the unit of lens power?
- (Chapter 8) What is the F2 ratio for Mendel's monohybrid cross?
- (Chapter 6) Where is the decision made in a reflex arc?
Answers — 1. Convex mirror | 2. 1/v + 1/u = 1/f | 3. Negative | 4. A change in speed when the medium changes | 5. Light travels slower in that medium; it is denser | 6. Concave lens | 7. 1/v − 1/u = 1/f | 8. Dioptre (D) | 9. 3:1 | 10. In the spinal cord
Glossary
| English | Hindi | English | Hindi |
|---|---|---|---|
| Concave mirror | अवतल दर्पण | Refraction | अपवर्तन |
| Convex mirror | उत्तल दर्पण | Refractive index | अपवर्तनांक |
| Principal focus | मुख्य फ़ोकस | Convex lens | उत्तल लेंस |
| Centre of curvature | वक्रता केंद्र | Concave lens | अवतल लेंस |
| Magnification | आवर्धन | Power of lens | लेंस की क्षमता |
| Sign convention | चिन्ह परिपाटी | Dioptre | डायोप्टर |
For parents and teachers
Five-minute check: Have them state both the mirror and lens formulas (stress the sign difference). Which mirror/lens always gives a small, virtual image? In what unit is lens power measured?
To try at home: a steel bowl (concave mirror), the back of a spoon (convex mirror), and a glass of water (refraction) — all three make for safe, visible experiments.
Beyond NCERT — For Curious Readers
This section goes beyond the RBSE/NCERT Class 10 syllabus and is not required for the board exam. It draws only on government and internationally reputed university sources, for curious readers who want to see where this chapter leads.
Ibn al-Haytham — the medieval founder of the science of optics
Long before Newton, the 11th-century scholar Ibn al-Haytham (also known in the West as Alhazen), working in Cairo, wrote the Book of Optics — widely regarded by historians of science as the first work to insist that light travels from an object to the eye (not the other way around, as many ancient thinkers believed) and to study reflection and refraction through careful, repeatable experiment rather than pure philosophical argument. He is credited with building an early version of the camera obscura — a darkened box or room with a small hole that projects an inverted image of the outside world onto an opposite wall, using exactly the straight-line propagation of light this chapter assumes throughout.
Snell's law — the precise mathematics behind refraction
NCERT describes refraction qualitatively — light bends when it changes medium — but the exact relationship was worked out by the Dutch astronomer Willebrord Snellius in the early 17th century (and, evidence suggests, independently by others before him). Snell's law states that n₁ sin θ₁ = n₂ sin θ₂, where θ₁ and θ₂ are the angles of incidence and refraction measured from the normal, and n₁, n₂ are the refractive indices of the two media. This single equation predicts exactly how much any ray bends at any interface — the refractive index this chapter introduces is precisely the n in Snell's own law.
Total internal reflection — when light refuses to leave
Refraction has a striking limit. When light travels from a denser medium (like glass or water) toward a rarer one (like air) at a large enough angle, it stops refracting out altogether and reflects entirely back inside the denser medium — a phenomenon called total internal reflection. The angle beyond which this happens is called the critical angle, and it depends directly on the refractive index of the medium — media with a higher refractive index have a smaller critical angle, making total internal reflection easier to achieve. This is precisely why diamonds, with their very high refractive index and a critical angle of only about 24°, trap and bounce light internally so many times before it escapes, producing their characteristic brilliance — an extension of exactly the "higher refractive index, more bending" idea introduced earlier in this chapter.
Fibre optics — total internal reflection at work worldwide
Total internal reflection is the working principle behind optical fibre cables — thin glass or plastic strands that guide light along their length by repeatedly reflecting it internally off the fibre's own walls, losing almost none of it even around bends. This technology now forms the backbone of most of the world's high-speed internet and telephone networks, carrying signals as pulses of light across oceans through undersea cables. India's Department of Telecommunications runs major fibre-optic infrastructure programmes such as BharatNet specifically to extend this same technology to rural India.
Mirages — refraction bending an entire landscape
On a hot road or in a desert, refraction can bend light on a much larger scale than a glass slab. Near the ground, intensely heated air is less dense (and has a lower refractive index) than the cooler air above it. Light from the sky, passing through this layered air, bends gradually and can curve upward into an observer's eye, creating the illusion of a shimmering "pool of water" on the road ahead — which is, in fact, a refracted image of the sky itself. This everyday phenomenon is essentially millions of tiny refractions, of exactly the kind studied with a single glass slab in this chapter, acting together through continuously changing air density.
Optical instruments built on this chapter's principles
Several everyday devices are direct, practical applications of spherical mirrors and lenses:
- Periscope — uses two plane mirrors set at 45°, applying the plain law of reflection to let a viewer see over an obstacle, used in submarines and trenches.
- Camera — uses a convex lens to form a real, inverted image on a film or digital sensor, precisely following the ray diagrams and lens formula covered in this chapter.
- Simple compound microscope — uses combinations of convex lenses, exploiting the magnifying-glass configuration (object between F1 and the optical centre) covered above, to view objects far too small for the naked eye.
Reflecting telescopes — concave mirrors on an astronomical scale
Large astronomical telescopes commonly use enormous concave mirrors rather than lenses, because a mirror can be supported from behind across its whole surface, while a large lens can only be held at its edges and tends to sag under its own weight. India's own major optical facility, the Indian Astronomical Observatory at Hanle in Ladakh, operates a large reflecting telescope built on this exact principle. On a much larger scale, the James Webb Space Telescope — launched in 2021 and operated by NASA together with the European and Canadian space agencies — uses a mirror over six metres across, made of 18 smaller hexagonal segments, applying precisely the same concave-mirror image-forming principle this chapter introduces with a simple steel bowl.
Sources for this section
- ncert.nic.in — NCERT, Government of India
- ePathshala — Ministry of Education, Government of India
- iiap.res.in — Indian Institute of Astrophysics
Note: nothing from these sources has been copied into this text; all statements above are written in the author's own words for general educational understanding, and are not medical, engineering, or professional advice.
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Related material
- Chapter 8 — Heredity (Hindi)
- Chapter 9 — प्रकाश: परावर्तन तथा अपवर्तन (Hindi)
- Class 10 Science Mega Test — 200 MCQs
Based on the Class 10 Science (Code 07) syllabus 2026–2027 of the Board of Secondary Education, Rajasthan, Ajmer — Chapter 9, marks weightage 8. Textbook: Science, NCERT. All diagrams are original.
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