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Class 10 Light notes: NCERT Science Chapter 9, Reflection and Refraction

CMDLearn · 4 November 2026

These are short revision notes for Chapter 9 of the NCERT Class 10 Science textbook, "Light – Reflection and Refraction" (Reprint 2026-27), pages 134 to 160. The chapter has two formulas that look alike and one sign convention that decides most marks, so these notes put the formulas side by side, then go through mirrors and lenses section by section, and end with the key words, the ray diagram to practise, the common mistakes and 8 quick questions of our own with worked answers.

Keep the textbook open next to these notes. The wording here is our own; the textbook is the authority.

How much it counts

CBSE's Class 10 Science curriculum for 2026-27 puts this chapter in Unit III, Natural Phenomena, worth 12 of the 80 theory marks, shared with The Human Eye and the Colourful World (curriculum, PDF page 4). For this chapter the unit lists reflection from curved surfaces, the images spherical mirrors form and the terms used for them, the mirror formula (no derivation), magnification, refraction and its laws, refractive index, images formed by spherical lenses, the lens formula (no derivation), magnification and the power of a lens (PDF page 5). More on the units: CBSE Class 10 Science syllabus 2026-27.

The formulas on one page

1. Reflection and spherical mirrors (sections 9.1-9.2, pages 134-137)

• Laws of reflection: the angle of incidence equals the angle of reflection, and the incoming ray, the reflected ray and the normal where the ray strikes all lie in one plane. They hold for curved mirrors too (page 135).
• A plane mirror gives an image that is virtual, erect and the same size, the same distance behind the mirror that the object stands in front of it, and laterally inverted (page 135).
• A concave mirror is curved inwards (its reflecting surface faces the centre of the sphere); a convex mirror is curved outwards (page 135).
• Terms (pages 135-137): pole P (centre of the reflecting surface), centre of curvature C (in front of a concave mirror, behind a convex one), radius of curvature R, principal axis (through P and C, normal to the mirror at P), principal focus F (where rays parallel to the axis meet after reflection, or seem to come from), focal length f (PF) and aperture (the diameter of the reflecting surface).
• For mirrors of small aperture, R = 2f: F lies midway between P and C (page 137).

2. Images by mirrors (pages 138-142)

Concave mirror (Table 9.1, page 138):

Convex mirror (Table 9.2, page 141): the image is always behind the mirror, between P and F (at F for an object at infinity), diminished, virtual and erect.

Rays for diagrams (pages 138-139): a ray parallel to the axis passes through F after reflection (concave) or seems to come from F (convex); a ray through F, or aimed at F, comes back parallel; a ray through C, or aimed at C, returns along itself; a ray striking P reflects at an equal angle to the axis.

Uses:

• Concave mirrors (page 140): torches, search-lights and vehicle headlights (parallel beams), shaving mirrors, dentists' mirrors, solar furnaces.
• Convex mirrors (page 142): rear-view (wing) mirrors, because the image is always erect and the field of view is wider.

3. Sign convention, mirror formula and magnification (pages 142-145)

New Cartesian Sign Convention (pages 142-143):

• the pole is the origin and the principal axis is the x-axis;
• the object is placed on the left;
• distances are measured from the pole;
• distances to the right are positive and to the left negative;
• heights above the axis are positive and below it negative.

So u is negative for a real object; f is negative for a concave mirror and positive for a convex one.

Mirror formula: 1/v + 1/u = 1/f, valid for every spherical mirror and every object position (page 143).

Magnification: m = h′/h = −v/u. A negative m means a real (inverted) image, and a positive m means a virtual (erect) image (page 143).

4. Refraction (section 9.3, pages 145-149)

• Light changes direction when it passes obliquely from one transparent medium into another: this is refraction. Examples include a pond that looks shallower, a pencil that looks bent in water, and a coin that reappears when water is poured into a bowl (pages 145-146).
• Glass slab (page 147): the ray bends towards the normal entering glass and away from it leaving; the emergent ray is parallel to the incident ray, but shifted sideways.
• Refraction happens because the speed of light changes between media (page 147).
• Laws of refraction (page 148): - the incoming ray, the bent (refracted) ray and the normal all lie in one plane; - sin i / sin r is constant for a given colour and pair of media (Snell's law). That constant is called the refractive index of medium 2 relative to medium 1.
• Refractive index (pages 148-149): - n₂₁ = speed in medium 1 ÷ speed in medium 2; - the absolute refractive index is n = c/v, with c = 3 × 10⁸ m/s; - Table 9.3 gives values such as water 1.33, crown glass 1.52 and diamond 2.42 (you need not learn them).
• Optical density (page 149): whichever medium has the higher refractive index is the optically denser one, and light is slower in it. This is not mass density: kerosene is optically denser than water but lighter.

5. Lenses, lens formula and power (pages 150-158)

• A convex lens is thicker in the middle and converges light; a concave lens is thicker at the edges and diverges it (page 150).
• Terms: centres of curvature C₁ and C₂, principal axis, optical centre O (a ray through it goes straight on), two principal foci F₁ and F₂, focal length and aperture (pages 150-151).
• Convex lens (Table 9.4, page 152): it gives the same pattern as a concave mirror, with 2F in place of C. The image is real and inverted for objects beyond F₁ and the same size at 2F₁. Between F₁ and O it is virtual, erect and enlarged, on the same side as the object.
• Concave lens (Table 9.5, page 153): the image is always virtual, erect and diminished, between F₁ and O.
• Ray rules (pages 153-154): parallel to the axis then through F (convex) or seeming to come from F (concave); through F, or aimed at it, then parallel; through O, undeviated.
• Sign convention for lenses (page 155): the same rules, with distances measured from O. A convex lens has a positive focal length and a concave lens a negative one.
• Lens formula: 1/v − 1/u = 1/f (page 155). Magnification: m = h′/h = v/u (page 156).
• Power (pages 157-158): - P = 1/f with f in metres, in dioptres (1 D = 1 m⁻¹); - convex lenses have positive power and concave lenses negative; - for lenses in contact the powers simply add.

Key words at a glance

• Principal focus: the point where rays parallel to the principal axis meet, or seem to meet, after reflection or refraction.
• Focal length: the distance from the pole (mirror) or optical centre (lens) to the principal focus.
• Real image: can be caught on a screen; inverted for a single mirror or lens.
• Virtual image: cannot be caught on a screen; erect.
• Magnification: image height ÷ object height.
• Refractive index: speed of light in one medium ÷ speed in the other.
• Optically denser medium: the one with the larger refractive index.
• Dioptre: the power of a lens of focal length 1 m.

The diagram to know: convex lens, object between F₁ and 2F₁

Board papers often ask for one lens ray diagram. Practise this one (it is one of the cases in Fig. 9.16):

1. Draw the principal axis and the lens at O; mark F₁ and 2F₁ on the left, F₂ and 2F₂ on the right, at equal spacing.
2. Draw the object as an upright arrow between F₁ and 2F₁.
3. From the top of the object, draw a ray parallel to the axis; after the lens, draw it through F₂.
4. From the same point, draw a ray through O, carrying straight on.
5. Where the two rays meet, beyond 2F₂, draw the image as an inverted arrow, larger than the object. Label it real, inverted, enlarged.

Mistakes that cost marks

• Using the mirror formula for a lens. Mirror: 1/v + 1/u = 1/f. Lens: 1/v − 1/u = 1/f.
• Forgetting the minus sign in mirror magnification. For mirrors m = −v/u; for lenses m = v/u.
• Positive u. A real object sits on the left, so u is negative in both formulas.
• Wrong sign of f. Concave mirror and concave lens: f negative. Convex mirror and convex lens: f positive.
• Power in centimetres. P = 1/f needs f in metres: f = 25 cm gives P = 1/0.25 = 4 D, not 1/25.
• Mixing optical density and mass density. Kerosene floats on water but bends light more.

Quick check: 8 questions of our own

These are our own questions, written for these notes and checked against the textbook pages named; no practising teacher has reviewed them yet. Every number was re-computed by a script.

Question 1. A concave mirror has a focal length of 12 cm. A 2 cm tall pin stands upright 8 cm away from it. (a) Write u and f with their signs. (b) Find the image distance. (c) Find the magnification and the image height. (d) Describe the image, and check it against the textbook's table.

Answer: (a) u = −8 cm, f = −12 cm; (b) v = +24 cm, behind the mirror; (c) m = +3, h′ = +6 cm; (d) virtual, erect, enlarged. (a) The object is on the left, and a concave mirror's focus is in front of it, so both are negative (pages 142-143). (b) 1/v = 1/f − 1/u = −1/12 + 1/8 = (−2 + 3)/24 = 1/24, so v = +24 cm. (c) m = −v/u = −24/(−8) = +3, so h′ = 3 × 2 = 6 cm (page 143). (d) A positive m means a virtual, erect image; Table 9.1 gives exactly this for an object between P and F (page 138).

Question 2. A convex mirror on a shop wall has a radius of curvature of 40 cm. A customer stands 30 cm in front of it. (a) What is its focal length, with sign? (b) Where is the image? (c) What is the magnification, and what is the image like?

Answer: (a) +20 cm; (b) 12 cm behind the mirror; (c) +0.4, virtual, erect and diminished. (a) f = R/2 = 40/2 = 20 cm, positive because a convex mirror's focus is behind it (pages 137, 143). (b) 1/v = 1/f − 1/u = 1/20 + 1/30 = 5/60 = 1/12, so v = +12 cm. (c) m = −v/u = −12/(−30) = +0.4. That fits Table 9.2: the image sits behind the mirror, between P and F, smaller than the object, virtual and erect (page 141).

Question 3. Say which mirror is needed, and where the object must be, in each case: (a) a sharp image of a candle the same size as the candle, inverted, on a screen; (b) a large, erect image of a tooth; (c) a mirror on a sharp hill bend that always shows an erect view of a wide stretch of road; (d) a real image of a distant streetlight formed as a tiny bright point.

Answer: (a) concave mirror, object at C; (b) concave mirror, object between P and F; (c) convex mirror; (d) concave mirror, image at F. (a) and (b) are rows of Table 9.1 (page 138); dentists use concave mirrors for (b) (page 140). (c) A convex mirror always gives an erect, diminished image and has a wider field of view (pages 141-142). (d) For an object at infinity a concave mirror forms a point-sized, real image at the focus (page 138).

Question 4. Use the refractive indices in Table 9.3 (page 149): ruby 1.71, water 1.33, crown glass 1.52, and c = 3 × 10⁸ m/s. (a) What is the speed of light in ruby? (b) A ray passes obliquely from water into crown glass. Does it bend towards or away from the normal? (c) What is the refractive index of crown glass with respect to water, to two decimal places?

Answer: (a) about 1.75 × 10⁸ m/s; (b) towards the normal; (c) about 1.14. (a) n = c/v, so v = c/n = 3 × 10⁸ ÷ 1.71 ≈ 1.75 × 10⁸ m/s (page 149). (b) Crown glass has the larger refractive index, so it is optically denser; light slows on entering a denser medium and so bends towards the normal (page 149). (c) n(glass, water) = speed in water ÷ speed in glass = (c/1.33) ÷ (c/1.52) = 1.52/1.33 ≈ 1.14 (pages 148-149).

Question 5. From Table 9.3 (page 149): ice 1.31, alcohol 1.36 and benzene 1.50. (a) Which of the three is optically densest? (b) In which does light travel fastest? (c) What is the speed of light in benzene, taking c = 3 × 10⁸ m/s? (d) Benzene's mass density is lower than water's. Does that mean benzene is optically rarer than water (1.33)?

Answer: (a) benzene; (b) ice; (c) 2 × 10⁸ m/s; (d) no, it is optically denser. (a) The highest refractive index marks the optically densest of the three (page 149). (b) Light is fastest where the refractive index is smallest, since v = c/n (page 149): ice, at about 3 × 10⁸ ÷ 1.31 ≈ 2.29 × 10⁸ m/s. (c) v = c/n = 3 × 10⁸ ÷ 1.50 = 2 × 10⁸ m/s. (d) Optical density is not mass density: 1.50 > 1.33, so benzene is optically denser than water whatever its mass density, just as the book says of kerosene (page 149).

Question 6. A 3 cm tall object is placed 18 cm from a convex lens of focal length 12 cm. (a) Find the image distance. (b) Find the magnification and the image height. (c) Describe the image, and check it against the textbook's table for a convex lens.

Answer: (a) v = +36 cm; (b) m = −2, h′ = −6 cm; (c) real, inverted, enlarged, on the other side of the lens. (a) u = −18 cm and f = +12 cm (page 155). 1/v = 1/f + 1/u = 1/12 − 1/18 = (3 − 2)/36 = 1/36, so v = +36 cm. (b) m = v/u = 36/(−18) = −2 (page 156), so h′ = −2 × 3 = −6 cm. (c) The negative sign means real and inverted. The object is between F₁ (12 cm) and 2F₁ (24 cm), and Table 9.4 puts the image beyond 2F₂ (here 36 cm > 24 cm), enlarged, real and inverted (page 152).

Question 7. An object is placed 30 cm from a concave lens of focal length 20 cm. (a) Where is the image? (b) What is the magnification? (c) Could you catch this image on a screen?

Answer: (a) 12 cm from the lens, on the same side as the object; (b) +0.4; (c) no. (a) u = −30 cm and f = −20 cm (concave lens, page 155). 1/v = 1/f + 1/u = −1/20 − 1/30 = −5/60 = −1/12, so v = −12 cm: on the object's side. (b) m = v/u = (−12)/(−30) = +0.4 (page 156). (c) A positive m and an image on the same side mean a virtual, erect, diminished image, as a concave lens always gives (pages 153, 156); virtual images cannot be caught on a screen.

Question 8. (a) An eye prescription reads −1.25 D. What kind of lens is it, and what is its focal length in cm? (b) A reading lens has a focal length of +40 cm. What is its power? (c) If these two lenses were placed in contact, what would be the power and the focal length of the combination?

Answer: (a) concave, f = −80 cm; (b) +2.5 D; (c) +1.25 D, f = +80 cm (convex). (a) Negative power means a concave lens; f = 1/P = 1/(−1.25) = −0.8 m = −80 cm (pages 157-158). (b) P = 1/f = 1/0.40 m = +2.5 D. (c) Powers of lenses in contact add: −1.25 + 2.5 = +1.25 D, so f = 1/1.25 = 0.8 m = +80 cm, a convex (converging) combination (page 158).

Revise with questions

Test yourself next: Class 10 Light, 8 practice questions with answers. The other notes in this set: Electricity, Acids, Bases and Salts and Life Processes. For timed practice, the free Class 10 revision papers include a Science paper laid out in 1, 2, 3 and 5-mark sections.

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Sources

All checked on 4 November 2026. NCERT page numbers are the printed page numbers of the textbook (printed page = PDF page + 133).

• NCERT, Science, Textbook for Class X, Chapter 9 "Light – Reflection and Refraction" (Reprint 2026-27), pages 134-160: section 9.1 (pages 134-135); 9.2 and Tables 9.1-9.2 (pages 135-142); sign convention, mirror formula and magnification (pages 142-145); 9.3, the glass slab, the laws of refraction and Table 9.3 (pages 145-149); lenses, Tables 9.4-9.5, the lens formula, magnification and power (pages 150-158). ncert.nic.in/textbook/pdf/jesc109.pdf
• CBSE, Science curriculum, Class X, 2026-27: unit marks (PDF page 4) and Unit III contents (PDF page 5): cbseacademic.nic.in/web_material/CurriculumMain27/SecPart1/Science_SecP1_2026-27.pdf

The facts, formulas, section numbers and figure numbers are from the documents above. The wording of these notes, the diagram steps, the list of mistakes and the 8 questions are our own.

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