Light – Reflection and Refraction

This is Chapter 9 of NCERT's Class 10 Science textbook (pages 134–160 of the 2026-27 reprint; the contents page and the PDF agree). It has two halves — reflection (9.1 the laws; 9.2 spherical mirrors, image formation, ray diagrams, the sign convention, mirror formula and magnification) and refraction (9.3: the glass slab, laws of refraction, refractive index, spherical lenses, lens images, lens formula, magnification and power) — with 13 activities, Figures 9.1–9.17, Tables 9.1–9.5, three ‘More to Know!’ boxes, 4 worked examples, four ‘Questions’ boxes and 17 exercise questions. It is the first physics chapter on this site: every ray diagram below is drawn from the mirror or lens formula and checked in the page's source, and every numerical answer is computed and asserted.

• Neighbouring chapters: the next chapter, The Human Eye and the Colourful World, uses these lenses and refraction for the eye, its defects and their correction (myopia, hypermetropia), the prism, dispersion, the rainbow, twinkling of stars and the blue sky. On this site, Sensory, Attentional and Perceptual Processes (Class 11 Psychology) covers what the eye and brain do with the image, and Solar Radiation, Heat Balance and Temperature and Composition and Structure of Atmosphere (Class 11 Geography) cover reflection of sunlight (albedo) and the atmosphere light passes through.
• Prelims — science: UPSC has asked why a pinhole forms an inverted image (rectilinear propagation, 1979), which mirror motorists use to see behind (convex, 1980), where light travels slowest (glass, 1994), why a cut diamond sparkles (its very high refractive index, 1994–95) and how far a reflected ray turns when a mirror is turned (twice the angle, 1996). Expect statements on mirror and lens uses, real vs virtual images, sign conventions, refractive index and optical density, and power in dioptres.
• GS3 — science and technology: optics behind everyday technology — headlights and search-lights, solar furnaces and solar concentrators, rear-view and blind-spot mirrors on roads, spectacles and contact lenses, cameras, microscopes and telescopes, and (Beyond this chapter) optical fibres for telecom and endoscopy.

• Light travels in straight lines (rays). Reflection: angle of incidence = angle of reflection, and incident ray, normal and reflected ray lie in one plane. A plane mirror's image is virtual, erect, same size, as far behind as the object is in front, laterally inverted.
• Concave mirror converges, convex diverges. Vocabulary: pole P, centre of curvature C, radius R, principal axis, principal focus F, focal length f, aperture. For small apertures R = 2f.
• Concave mirror (Table 9.1): object beyond F → real, inverted image (diminished beyond C, same size at C, enlarged between C and F); at F → no image; inside F → virtual, erect, enlarged. Convex mirror: always virtual, erect, diminished, between P and F — rear-view mirrors.
• New Cartesian sign convention: pole/optical centre is the origin, light comes from the left, right and up are positive. Mirror: 1/v + 1/u = 1/f, m = h′/h = −v/u. Negative m ⇒ real and inverted.
• Refraction = bending because light changes speed. Snell's law: sin i / sin r = constant = refractive index. n = c/v; c = 3 × 10⁸ m s⁻¹. Rarer → denser bends towards the normal. A glass slab shifts a ray sideways but keeps it parallel. Optical density ≠ mass density (kerosene vs water).
• Convex lens converges (like a concave mirror, Table 9.4); concave lens always gives a virtual, erect, diminished image. Lens: 1/v − 1/u = 1/f, m = v/u. Power P = 1/f (f in metres), unit dioptre (D): convex +, concave −; powers in contact add.

A highly polished surface such as a mirror reflects most of the light falling on it. NCERT recalls the two laws of reflection: (i) the angle of incidence equals the angle of reflection; (ii) the incident ray, the normal at the point of incidence and the reflected ray all lie in the same plane. These laws apply to every reflecting surface, curved ones included. A plane mirror gives an image that is virtual and erect, the same size as the object, as far behind the mirror as the object is in front, and laterally inverted (left and right swapped).

A spherical mirror has a reflecting surface that is part of a sphere. If it is curved inwards, facing the centre of the sphere, it is concave; if curved outwards, convex; in diagrams the back is shaded. The terms: the pole (P) is the centre of the reflecting surface and lies on the mirror; the centre of curvature (C) is the centre of the sphere — not on the mirror, in front of a concave mirror and behind a convex one; the radius of curvature (R) = PC; the principal axis passes through P and C and is normal to the mirror at P; the aperture is the diameter of the reflecting surface (MN). Rays parallel to the principal axis, after reflection, meet at the principal focus F of a concave mirror, or appear to come from F behind a convex mirror; f = PF. For mirrors whose aperture is much smaller than R, R = 2f — F is midway between P and C.

Activity 9.3 marks chalk lines for P, F and C on a table (one focal length apart) and moves a candle from far beyond C to inside F, catching the flame's image on a screen. The image is real for every position beyond F and virtual for an object between P and F — then it cannot be caught on the screen and is seen in the mirror itself. NCERT summarises the results in Table 9.1 (below, every row checked with the mirror formula for f = 10 cm).

Ray diagrams. Every point of an object sends out countless rays, but two well-chosen ones are enough: where they meet (or seem to meet) after reflection is the image of that point. NCERT gives four: (i) a ray parallel to the axis reflects through F (concave) or as if from F (convex); (ii) a ray through F (or aimed at F of a convex mirror) reflects parallel to the axis; (iii) a ray through C (or aimed at C) strikes along the normal and returns along the same path; (iv) a ray striking the pole reflects at an equal angle on the other side of the axis.

Uses of concave mirrors (page 140): torches, search-lights and vehicle headlights (a bulb at F sends out a powerful parallel beam); shaving mirrors (face inside F → enlarged erect image); dentists' mirrors (large images of teeth); and large concave mirrors in solar furnaces to concentrate sunlight.

NCERT considers two positions (Figure 9.8, Table 9.2): an object at infinity gives a point-sized image at F behind the mirror; an object anywhere between infinity and P gives a diminished image between P and F behind the mirror — in both cases virtual and erect. In Activity 9.5 you move a pencil away from a convex mirror and watch the image shrink. Activity 9.6 compares mirrors for a full-length image of a distant tree: a plane mirror needs to be large, a concave mirror inverts or enlarges, but a small convex mirror shows the whole tree. NCERT's example: a convex mirror fitted in a wall of Agra Fort facing the Taj Mahal shows its full image.

Uses of convex mirrors: rear-view (wing) mirrors of vehicles, because they always give an erect, though diminished, image and have a wider field of view than a plane mirror of the same size (in-text page 142 Q4; exercise 8b).

The New Cartesian Sign Convention (Figure 9.9): (i) the object is always placed to the left of the mirror, so light falls on it from the left; (ii) all distances parallel to the principal axis are measured from the pole; (iii) distances to the right of the origin are positive, to the left negative; (iv) heights above the axis positive; (v) heights below negative. So u is always negative; f is negative for a concave mirror and positive for a convex one.

The mirror formula (9.1) links object distance u, image distance v and focal length f: 1/v + 1/u = 1/f, valid for all spherical mirrors and all object positions when the signs are used. Magnification m = h′/h (9.2) = −v/u (9.3). Object height is taken positive; image height is positive for virtual (erect) images and negative for real (inverted) ones — so negative m means real, positive m means virtual.

Everyday clues: the bottom of a tank or pond looks raised; letters under a thick glass slab look raised; a pencil partly in water looks displaced at the surface; a lemon in a glass of water looks bigger from the side. The effect differs for different pairs of media (water, kerosene, turpentine; glass vs plastic). So light, travelling obliquely from one medium into another, changes direction: refraction. Activity 9.7 (picking a coin from a bucket of water in one go), Activity 9.8 (a coin in a bowl that reappears when water is poured in) and Activity 9.9 (a line seen through a glass slab looks bent at the edges and raised from above) all show it. Refraction is caused by the change in the speed of light from one medium to another.

Refraction through a rectangular glass slab (Activity 9.10, Figure 9.10): a ray EO enters the slab at O, going from a rarer to a denser medium, and bends towards the normal; inside, OO′ is the refracted ray; at O′ it leaves glass for air, denser to rarer, and bends away from the normal; O′H is the emergent ray. The bending at the two parallel faces is equal and opposite, so the emergent ray is parallel to the incident ray but shifted sideways slightly. A ray striking the surface normally (i = 0) goes straight through without bending.

The laws of refraction: (i) the incident ray, the refracted ray and the normal at the point of incidence lie in one plane; (ii) for light of a given colour and a given pair of media, sin i / sin r = constant (9.4) — Snell's law, true for 0 < i < 90°. The constant is the refractive index of the second medium with respect to the first.

Light is fastest in vacuum, 3 × 10⁸ m s⁻¹; only marginally slower in air; considerably slower in glass or water. If v₁ and v₂ are the speeds in media 1 and 2, the refractive index of 2 with respect to 1 is n₂₁ = v₁/v₂ (9.5) and of 1 with respect to 2, n₁₂ = v₂/v₁ (9.6). With medium 1 as vacuum or air, n₂ is the absolute refractive index: n_m = c/v (9.7) — simply called the refractive index. Water n_w = 1.33; crown glass n_g = 1.52.

A lens is a transparent material bound by two surfaces of which one or both are spherical. A double convex (convex) lens bulges outwards, is thicker at the middle and converges light; a double concave (concave) lens is curved inwards, thicker at the edges, and diverges light. Each surface is part of a sphere whose centre is a centre of curvature (C₁, C₂); the line through them is the principal axis; the lens's central point is the optical centre O — a ray through O passes undeviated. The effective diameter is the aperture; the chapter deals only with thin lenses of small aperture. Parallel rays converge to (or appear to diverge from) a principal focus; a lens has two, F₁ and F₂, one on each side, at the focal length f from O.

Ray rules for lenses (Figs 9.13–9.15): (i) a ray parallel to the axis passes through F₂ after a convex lens, or appears to diverge from F₁ on the same side after a concave lens; (ii) a ray through F₁ of a convex lens (or aimed at F₂ of a concave lens) emerges parallel; (iii) a ray through the optical centre goes straight on.

Activity 9.12 draws five chalk lines one focal length apart (2F₁, F₁, O, F₂, 2F₂) and moves a candle from far beyond 2F₁ to inside F₁; Table 9.4 summarises the convex lens. Activity 9.13 shows that a concave lens always gives a virtual, erect and diminished image, whatever the object's position (Table 9.5).

For lenses the same sign rules apply, with all distances measured from the optical centre; a convex lens has positive f, a concave lens negative f. The lens formula (9.8): 1/v − 1/u = 1/f, valid for any spherical lens. Magnification m = h′/h (9.9) = v/u (9.10).

Power expresses the degree of convergence or divergence: P = 1/f (9.11). Its SI unit is the dioptre (D) when f is in metres: 1 D is the power of a lens of focal length 1 m; 1 D = 1 m⁻¹. A convex lens has positive power, a concave lens negative. NCERT's examples: +2.0 D → convex, f = +0.50 m; −2.5 D → concave, f = −0.40 m.

The chapter sets questions inside its 13 activities and in four ‘Questions’ boxes (pages 142, 145, 150 and 158). Outlines follow, in page order; every number is computed in the page's source.

Try each question first, then open the outline. Every number below is computed and checked against the book's answer key; the three ray diagrams NCERT asks for are drawn to scale after the outlines.

Numbers

One-liners

• We see objects because light reflected from them enters our eyes; light seems to travel in straight lines.
• Plane mirror image: virtual, erect, same size, as far behind as the object is in front, laterally inverted; m = +1.
• Concave mirror converges, convex mirror diverges; C and F in front of a concave mirror, behind a convex one.
• Concave mirror: real and inverted for objects beyond F; virtual, erect, enlarged inside F.
• Convex mirror and concave lens: always virtual, erect, diminished.
• Concave mirrors: torches, search-lights, headlights, shaving and dentists' mirrors, solar furnaces. Convex mirrors: rear-view mirrors.
• New Cartesian convention: origin at P or O; light from the left; right and up positive; u always negative.
• Negative magnification = real and inverted; positive = virtual and erect.
• Refraction is caused by the change in speed of light between media.
• Rarer → denser: bends towards the normal; denser → rarer: away.
• A glass slab gives an emergent ray parallel to the incident ray, shifted sideways.
• Optically denser = higher refractive index, not higher mass density (kerosene vs water).
• Convex lens: object at 2F₁ gives a same-size real image at 2F₂.
• Power of a convex lens is positive, of a concave lens negative; powers in contact add.

Traps to avoid

• Mirror formula has a PLUS (1/v + 1/u); lens formula a MINUS (1/v − 1/u). Mirror m = −v/u; lens m = +v/u.
• Real image: v negative for a mirror (in front) but positive for a lens (other side).
• Concave MIRROR and convex LENS converge; convex mirror and concave lens diverge.
• A concave mirror CAN give an erect enlarged image (object inside F); a convex mirror never gives a real image.
• Kerosene is optically denser than water though lighter by mass — optical density ≠ mass density.
• Higher n means SLOWER light; light is fastest in water among water, kerosene and turpentine.
• Half-covered lens: complete but dimmer image.
• Convert focal length to metres before P = 1/f (25 cm → +4 D).
• Turning a mirror by θ turns the reflected ray by 2θ.
• NCERT slips: Example 9.2 cites ‘Eq. (10.1)’ (it is 9.1); the key's 2.2 cm in exercise 14 is 2.1 cm exactly; C is not at 2F for a lens, whatever Figs 9.12 and 9.16 suggest.

Prelims — what UPSC asks

• Mirror uses: the convex rear-view mirror was asked as early as 1980. Learn the use-list both ways — concave for headlights, search-lights, shaving and dentists' mirrors and solar furnaces; convex for rear-view mirrors — and the reason for each (parallel beam, enlarged erect image, concentrated heat, wide erect view).
• Refractive index and speed: 1994 asked where light is slowest (glass, of glass, vacuum, water, air); 1994 and 1995 asked about a diamond's sparkle (very high refractive index; an A/R where the reason ‘diamond's n is less than glass’ is false). Table 9.3's order and v = c/n answer all three; the full mechanism (total internal reflection) is Class 12.
• Straight-line travel and the laws of reflection: 1979 (a pinhole's inverted image = rectilinear propagation) and 1996 (mirror turned by θ → reflected ray by 2θ).
• Likely next: real vs virtual image statements; which mirror or lens gives an erect magnified image; power and dioptre arithmetic for spectacles; optical density vs mass density; refraction examples (raised pond bottom, bent pencil). Related favourites — total internal reflection, optical fibres, endoscopy, mirages — need Class 12 Physics on top of this chapter.

Mains — where it appears and how to answer

• No GS Mains question in the bank so far is built on this chapter. Its use in GS3 is as the science line in applied answers: optical-fibre broadband (Beyond this chapter: total internal reflection), solar concentrators and solar furnaces (concave mirrors), road safety (convex mirrors at blind spots), and eye care and spectacles (lens power — next chapter).
• Answer frame for a science-and-technology question: one-line principle (reflection/refraction, with the governing formula) → technology that uses it → its Indian application → limits or concerns → way forward. A neat labelled ray diagram takes a minute and lifts the answer.

Tap an option. NCERT's own exercise questions come first; the rest test the figures and common confusions.

Open any question to attempt it in the Question bank — your attempt is saved to your progress.