BharatNotes Why this chapter matters for UPSC: This is Chapter 9, "Light – Reflection and Refraction", of NCERT's Class X Science (Reprint 2026-27). It is a numbers chapter: where a mirror or lens puts an image, how big it is, whether it is real, and how a single sign convention turns all of that into two formulae. Prelims asks the image tables, the refractive-index order and the dioptre directly; GS3 science and technology builds on the same physics when it asks about optical fibre, telescopes and quantum technologies.
Contemporary hook: In a Lok Sabha reply of 17 December 2025, the Ministry of Communications said the Amended BharatNet Program, approved by the Union Cabinet on 4 August 2023, is to give optical fibre connectivity to about 2.64 lakh gram panchayats and about 3.8 lakh non-GP villages on demand. The signal in that fibre is light, kept inside the glass by the reflection and refraction this chapter starts.
🧠 First Principles — Read This First
- Light travels in straight lines for everything in this chapter. NCERT's opening box adds that light also bends round very small objects (diffraction) and that a "modern quantum theory of light" treats it as neither a wave nor a particle; the chapter then works with straight rays only (p. 134).
- Reflection sends light back into the same medium; refraction is the change of direction when light passes from one transparent medium into another, because its speed changes.
- Real or virtual. A real image is formed where rays actually meet and can be caught on a screen; a virtual image is where rays only appear to come from.
- One sign convention (distances measured from the pole or optical centre, along the incident light positive) lets one formula cover every position of the object.
- Refractive index compares the speed of light in two media; the larger it is, the more "optically dense" the medium and the more the light bends towards the normal on entering it.
- Power of a lens is the reciprocal of its focal length in metres; it is how an optician writes a prescription.
PART 1 — Quick Reference
Table 1: Reflection and spherical mirrors (9.1-9.2)
| Idea | What NCERT says |
|---|---|
| Laws of reflection | Angle of incidence equals angle of reflection; the incident ray, the normal at the point of incidence and the reflected ray all lie in the same plane. The laws apply to all reflecting surfaces, spherical ones included |
| Plane mirror image | Virtual and erect, same size as the object, as far behind the mirror as the object is in front, and laterally inverted |
| Concave and convex | Concave: reflecting surface curved inwards (towards the centre of the sphere). Convex: curved outwards |
| Pole (P), centre of curvature (C) | P = centre of the reflecting surface. C = centre of the sphere of which the mirror is a part; it lies in front of a concave mirror and behind a convex mirror |
| Radius of curvature (R), principal axis | R = radius of that sphere; the principal axis is the straight line through P and C |
| Principal focus (F), focal length (f) | Rays parallel to the axis meet at F after reflection (concave) or appear to come from F (convex); f = distance P to F |
| R = 2f | Holds "for spherical mirrors of small apertures" |
| Aperture | The diameter of the reflecting surface |
Source: NCERT, Science Class X, ch. 9, Reprint 2026-27, sections 9.1-9.2 (pp. 135-137).
Table 2: Image formed by a concave mirror (NCERT Table 9.1)
| Position of the object | Position of the image | Size of the image | Nature of the image |
|---|---|---|---|
| At infinity | At the focus F | Highly diminished, point-sized | Real and inverted |
| Beyond C | Between F and C | Diminished | Real and inverted |
| At C | At C | Same size | Real and inverted |
| Between C and F | Beyond C | Enlarged | Real and inverted |
| At F | At infinity | Image would not be formed | (none given) |
| Between P and F | Behind the mirror | Enlarged | Virtual and erect |
Source: NCERT, Science Class X, ch. 9, Reprint 2026-27, Table 9.1 (p. 138).
Table 3: Image formed by a convex mirror (NCERT Table 9.2), and where each mirror is used
| Position of the object | Position of the image | Size | Nature |
|---|---|---|---|
| At infinity | At the focus F, behind the mirror | Highly diminished, point-sized | Virtual and erect |
| Between infinity and the pole P | Between P and F, behind the mirror | Diminished | Virtual and erect |
| Mirror | Uses NCERT lists |
|---|---|
| Concave | Torches, search-lights and vehicle headlights (powerful parallel beams); shaving mirrors (larger image of the face); dentists (large image of teeth); large concave mirrors concentrate sunlight in solar furnaces |
| Convex | Rear-view (wing) mirrors of vehicles: always an erect, though diminished, image and a wider field of view because the mirror is curved outwards |
Source: NCERT, Science Class X, ch. 9, Reprint 2026-27, Table 9.2 and section 9.2.2 (pp. 140-142).
Table 4: Sign convention and the formulae
| Rule or formula | Mirrors | Lenses |
|---|---|---|
| Origin | Pole P | Optical centre O |
| Object | Always placed to the left, so light falls from the left | Same |
| Distances along the axis | Measured from the origin; to the right (direction of incident light) positive, to the left negative | Same |
| Heights | Above the principal axis positive, below negative | Same |
| Focal length sign | Concave negative (F in front); convex positive (F behind) | Convex positive; concave negative |
| Formula | 1/v + 1/u = 1/f (Eq. 9.1) | 1/v − 1/u = 1/f (Eq. 9.8) |
| Magnification | m = h′/h = −v/u (Eqs. 9.2-9.3) | m = h′/h = v/u (Eqs. 9.9-9.10) |
| Reading m | Negative m: real (inverted) image; positive m: virtual (erect) | Same reading |
| Power | Not used | P = 1/f (Eq. 9.11), f in metres, unit dioptre (D); 1 D = 1 m⁻¹ |
Source: NCERT, Science Class X, ch. 9, Reprint 2026-27, sections 9.2.3-9.2.4, 9.3.6-9.3.8 (pp. 142-143, 155-158).
Table 5: Refraction (9.3)
| Idea | What NCERT says |
|---|---|
| Everyday signs | A tank's bottom looks raised; letters under a thick glass slab look raised; a pencil in water looks displaced at the surface; a lemon in a glass of water looks bigger |
| Air to glass | The ray bends towards the normal |
| Glass to air | The ray bends away from the normal |
| Rectangular glass slab | The emergent ray is parallel to the incident ray but "shifted sideward slightly" |
| Cause | A change in the speed of light from one medium to the next |
| First law | Incident ray, refracted ray and the normal at the point of incidence lie in one plane |
| Second law (Snell's law) | sin i / sin r = constant, "for the light of a given colour and for the given pair of media"; the constant is the refractive index of the second medium with respect to the first (Eq. 9.4) |
| Relative index | n₂₁ = v₁/v₂ (Eq. 9.5); n₁₂ = v₂/v₁ (Eq. 9.6) |
| Absolute index | nₘ = c/v (Eq. 9.7); light's speed is 3 × 10⁸ m s⁻¹ in vacuum and only marginally less in air |
Source: NCERT, Science Class X, ch. 9, Reprint 2026-27, sections 9.3-9.3.2 (pp. 145-149).
Table 6: Absolute refractive indices (NCERT Table 9.3)
| Medium | n | Medium | n |
|---|---|---|---|
| Air | 1.0003 | Canada balsam | 1.53 |
| Ice | 1.31 | Rock salt | 1.54 |
| Water | 1.33 | Carbon disulphide | 1.63 |
| Alcohol | 1.36 | Dense flint glass | 1.65 |
| Kerosene | 1.44 | Ruby | 1.71 |
| Fused quartz | 1.46 | Sapphire | 1.77 |
| Turpentine oil | 1.47 | Diamond | 2.42 |
| Benzene | 1.50 | ||
| Crown glass | 1.52 |
NCERT adds that "you need not memorise the data": the use is to compare. Diamond has the highest value in the table and air the lowest.
Source: NCERT, Science Class X, ch. 9, Reprint 2026-27, Table 9.3 (p. 149).
Table 7: Images formed by lenses (NCERT Tables 9.4 and 9.5)
| Lens | Position of the object | Position of the image | Size | Nature |
|---|---|---|---|---|
| Convex | At infinity | At the focus F₂ | Highly diminished, point-sized | Real and inverted |
| Convex | Beyond 2F₁ | Between F₂ and 2F₂ | Diminished | Real and inverted |
| Convex | At 2F₁ | At 2F₂ | Same size | Real and inverted |
| Convex | Between F₁ and 2F₁ | Beyond 2F₂ | Enlarged | Real and inverted |
| Convex | At focus F₁ | At infinity | Image would not be formed | (none given) |
| Convex | Between F₁ and optical centre O | On the same side of the lens as the object | Enlarged | Virtual and erect |
| Concave | At infinity | At the focus F₁ | Highly diminished, point-sized | Virtual and erect |
| Concave | Between infinity and O | Between F₁ and O | Diminished | Virtual and erect |
A concave lens "will always give a virtual, erect and diminished image, irrespective of the position of the object" (p. 153).
Source: NCERT, Science Class X, ch. 9, Reprint 2026-27, Tables 9.4 and 9.5 (pp. 152-153).
Table 8: NCERT's worked examples
| Example | Data | Result |
|---|---|---|
| 9.1 Convex rear-view mirror | R = +3.00 m, bus at u = −5.00 m | f = +1.50 m; v = +1.15 m (behind the mirror); m = +0.23: virtual, erect, diminished |
| 9.2 Concave mirror | h = +4.0 cm, u = −25.0 cm, f = −15.0 cm | v = −37.5 cm (in front); h′ = −6.0 cm: real, inverted, enlarged |
| 9.3 Concave lens | f = −15 cm, image at v = −10 cm | u = −30 cm; m = +0.33: virtual, erect, one-third the size |
| 9.4 Convex lens | h = +2.0 cm, f = +10 cm, u = −15 cm | v = +30 cm; h′ = −4.0 cm; m = −2: real, inverted, two times enlarged |
| Power | +2.0 D; −2.5 D | f = +0.50 m (convex); f = −0.40 m (concave) |
| Lenses in contact | +2.0 D with +0.25 D | Net power +2.25 D |
Source: NCERT, Science Class X, ch. 9, Reprint 2026-27, Examples 9.1-9.4 and section 9.3.8 (pp. 144-145, 156-158).
Table 9: NCERT lines to read with care
| Where | What the book prints | How to read it |
|---|---|---|
| Example 9.2 (p. 144) | "From Eq. (10.1)" | The mirror formula is Eq. (9.1) in this edition; "10.1" is the number from the 2020-21 edition, where Light was Chapter 10 |
| Section 9.3.2 (p. 149) and Summary (p. 159) | The formula nₘ = c/v takes c as the speed of light in air; the summary defines refractive index with the speed in vacuum | NCERT itself says the two speeds differ only marginally |
| Snell's law (p. 148) | "(This is true for angle 0 < i < 90o)" | The printed "90o" is 90°; the law is stated for angles of incidence between 0° and 90° |
| Table 9.3 (p. 149) and Class XII | Dense flint glass 1.65 in Class X; 1.62 in NCERT's Class XII Table 9.1 | Two NCERT books give different values; the Class X book asks you not to memorise the data |
| Tables 9.1 and 9.4 (pp. 138, 152) | Object at F: image "At infinity" yet "Image would not be formed" | Rays from the focus leave parallel and never meet at a finite distance; the 2020-21 edition called this image highly enlarged, real and inverted |
Source: NCERT, Science Class X, ch. 9, Reprint 2026-27 (pp. 138-159); NCERT, Physics Part II, Class XII, ch. 9, Table 9.1.
PART 2 — Concepts & Narrative
Reflection and the plane mirror (9.1)
A highly polished surface such as a mirror reflects most of the light falling on it. The two laws of reflection hold for every reflecting surface, flat or curved; at each point of a curved mirror the "normal" is simply the normal to the surface at that point. A plane mirror's image is virtual, erect, of the same size, as far behind the mirror as the object is in front, and laterally inverted (left and right swapped).
Spherical mirrors and their images (9.2-9.2.2)
A spoon shows both kinds: the inner face bulges away from you and acts as a concave mirror, the outer face as a convex one. Each mirror is a piece of a sphere, which gives it a centre of curvature C and a radius R. For mirrors of small aperture, the principal focus F lies midway between P and C, so R = 2f.
NCERT draws images with four rays, any two of which locate the image: a ray parallel to the principal axis passes through F after reflection (concave) or appears to diverge from F (convex); a ray through F (concave) or directed towards F (convex) comes out parallel to the axis; a ray through C (concave) or directed towards C (convex) returns along its own path; a ray striking the pole obliquely is reflected at an equal angle on the other side of the axis.
Read Table 2 as one movement. As a candle walks from far away towards a concave mirror, its real, inverted image walks outwards from F, passes C at equal size, grows beyond C, is lost to infinity when the candle reaches F, and then reappears behind the mirror as a virtual, erect, enlarged image. That last row is the shaving mirror and the dentist's mirror. A convex mirror never produces a real image: whatever the distance, the image sits behind it between P and F, erect and smaller, which is why it is the rear-view mirror.
Why an object at F gives no image. By the second ray rule, every ray from the focus leaves a concave mirror (or a convex lens) parallel to the principal axis. Parallel rays do not meet at any finite distance, so the 2026 tables say the image is "At infinity" and "Image would not be formed". The 2020-21 edition had printed the same row as a highly enlarged, real and inverted image at infinity. Treat the current wording as the answer for exams set on the current book.
Sign convention, mirror formula and magnification (9.2.3-9.2.4)
NCERT's New Cartesian Sign Convention makes the pole the origin and the principal axis the x-axis. The object is always on the left. Distances measured in the direction of the incident light (to the right) are positive; against it, negative. Heights above the axis are positive, below negative.
New Cartesian Sign Convention. With the object on the left, u is always negative. For a concave mirror f is negative; for a convex mirror f is positive. A real image of a mirror lies in front of it, so its v is negative; a virtual image lies behind, so v is positive. Real images are inverted, so h′ and m are negative; virtual images are erect, so m is positive. The same rules, with the optical centre as origin, apply to lenses.
The mirror formula 1/v + 1/u = 1/f "is valid in all situations for all spherical mirrors for all positions of the object" (p. 143), provided every value carries its sign. Magnification m = h′/h = −v/u tells two things at once: its size says how much larger or smaller the image is, and its sign says whether the image is real (negative) or virtual (positive).
Example 9.1 is NCERT's rear-view mirror: a convex mirror of R = 3.00 m and a bus 5.00 m away give an image 1.15 m behind the mirror, about a quarter of the bus's size (m = +0.23). Example 9.2 places a 4.0 cm needle 25.0 cm from a concave mirror of focal length 15.0 cm: the image forms 37.5 cm in front, 6.0 cm tall and inverted.
Refraction and the glass slab (9.3-9.3.1)
Light that passes from air into glass slows down and bends towards the normal; leaving the glass, it speeds up and bends away. Through a rectangular slab the two bends cancel in direction, so the emergent ray runs parallel to the incident ray, displaced a little sideways. NCERT's words are "shifted sideward slightly"; the term "lateral displacement" used in many guides is not in this book.
The two laws of refraction are NCERT's statement of Snell's law: the rays and the normal lie in one plane, and sin i / sin r is a constant for a given colour of light and a given pair of media.
Refractive index (9.3.2)
The constant in Snell's law is the refractive index. NCERT defines it through speeds: n₂₁ = v₁/v₂, the speed in medium 1 over the speed in medium 2. Taking medium 1 as air or vacuum gives the absolute refractive index, nₘ = c/v. A value of 2.42 for diamond means the speed of light in vacuum is 2.42 times its speed in diamond (c/v = 2.42).
Optical density is not mass density. NCERT's "More to Know" box (p. 149) says optical density "is not the same as mass density". A medium with the larger refractive index is optically denser; light entering it from a rarer medium slows down and bends towards the normal. Kerosene (n = 1.44) is optically denser than water (n = 1.33) even though its mass density is lower.
Lenses and their images (9.3.3-9.3.5)
A lens has two refracting surfaces, at least one of them spherical. A convex lens is thicker at the middle and converges parallel rays; a concave lens is thicker at the edges and diverges them. Each surface has its own centre of curvature (C₁, C₂). Light through the optical centre O passes undeviated. NCERT works only with thin lenses of small aperture. A lens has two principal foci, F₁ and F₂, one on each side. In NCERT's Activity 9.11 a convex lens focuses sunlight on a sheet of paper, which begins to burn: the bright spot is a real image of the Sun, and its distance from the lens gives the approximate focal length (p. 151).
Ray rules for lenses are three: a ray parallel to the axis passes through F₂ after refraction (convex) or appears to come from F₁ (concave); a ray through F₁ (convex) or heading for F₂ (concave) emerges parallel; a ray through O goes straight on.
Table 7 repeats the mirror story with F₁ and 2F₁ in place of F and C. A convex lens forms real, inverted images for every object beyond F₁; with the object inside F₁ it gives a virtual, erect, enlarged image on the object's own side, which is the reading glass of NCERT's Exercise 6. A concave lens, like a convex mirror, only ever gives a virtual, erect, diminished image.
Lens formula, magnification and power (9.3.6-9.3.8)
The lens formula 1/v − 1/u = 1/f is "general and is valid in all situations for any spherical lens" (p. 155). For a lens, magnification is m = h′/h = v/u, without the minus sign of the mirror formula. Example 9.3 (concave lens, f = −15 cm, image at −10 cm) gives u = −30 cm and m = +0.33; Example 9.4 (convex lens, f = +10 cm, object 2.0 cm tall at −15 cm) gives v = +30 cm and an inverted image 4.0 cm tall (m = −2).
Why the minus sign is in one formula and not the other. For a mirror the real image forms on the same side as the object, so a real image has the same sign of distance as the object (both negative) and m = −v/u comes out negative. For a lens the real image forms on the far side, so v is positive while u is negative, and m = v/u comes out negative without an extra sign. Either way, a negative m means a real, inverted image.
The degree of convergence or divergence of a lens is its power, P = 1/f. A short focal length means a high power.
Dioptre and lenses in contact. "1 dioptre is the power of a lens whose focal length is 1 metre", so 1 D = 1 m⁻¹. Convex lenses have positive power, concave lenses negative. When lenses are "placed in contact", the net power is the algebraic sum of their powers, which is how an optician builds up a prescription in a trial frame (+2.0 D + 0.25 D = +2.25 D) and how lens systems in cameras, microscopes and telescopes are designed (p. 158). The sum rule is for lenses in contact; lenses set apart do not simply add.
Did the 2020-21 edition differ?
Yes, in two rows and in the numbering. Light was Chapter 10 in the 2020-21 edition and is Chapter 9 now. In the concave-mirror table, the row "At F" read "At infinity | Highly enlarged | Real and inverted"; in the convex-lens table, the row "At focus F₁" read "At infinity | Infinitely large or highly enlarged | Real and inverted". Both rows now say "Image would not be formed". The rest of the chapter reads the same, which is why Example 9.2 still points to "Eq. (10.1)".
Source: NCERT, Science Class X, 2020-21 edition (whole-book zip, Wayback Machine capture of 9 October 2021), compared with Reprint 2026-27.
Beyond the textbook: what Class XII adds (critical angle and optical fibres)
- Total internal reflection is not in the Class X book. Class XII defines the critical angle as the angle of incidence for which the angle of refraction is 90°; beyond it, light going from a denser to a rarer medium is wholly reflected, and "no transmission of light takes place".
- Class XII's Table 9.1 gives critical angles with respect to air: water (n 1.33) 48.75°; crown glass (1.52) 41.14°; dense flint glass (1.62) 37.31°; diamond (2.42) 24.41°. A higher refractive index means a smaller critical angle.
- An optical fibre has a core of higher refractive index than its cladding. Light entering at a suitable angle undergoes repeated total internal reflections, with "no appreciable loss in the intensity", even when the fibre is bent; Class XII calls it an "optical pipe".
- Class XII's summary also lists the sparkle of diamond, totally reflecting prisms and the mirage among the effects of total internal reflection.
Source: NCERT, Physics Part II, Textbook for Class XII, ch. 9 "Ray Optics and Optical Instruments", section 9.4, Table 9.1 and Summary (Reprint 2025-26).
Beyond the textbook: light in India's networks and laboratories
- BharatNet. The Amended BharatNet Program (ABP) was approved by the Union Cabinet on 4 August 2023 "to provide optical fiber connectivity to ~2.64 lakh Gram Panchayats (GPs) and ~3.8 lakh non-GP villages on demand basis" (Lok Sabha reply, 17 December 2025). The GPs are to be linked in a ring topology using MPLS technology, with BSNL as the Project Management Agency (June 2025). PIB's December 2024 backgrounder put the cost of the design improvement in ABP at Rs 1,39,579 crore.
- National Quantum Mission. Approved by the Union Cabinet on 19 April 2023 for 2023-24 to 2030-31 with ₹6,003.65 crore. Its targets include intermediate-scale quantum computers of 20-50 physical qubits in three years, 50-100 in five and 50-1000 in eight. Four Thematic Hubs (T-Hubs) have been set up at IISc Bengaluru, IIT Madras (with C-DOT), IIT Bombay and IIT Delhi, covering quantum computing, communication, sensing and metrology, and materials and devices. NCERT's opening box is the link: the quantum theory of light.
- Devasthal Optical Telescope. The 3.6-metre DOT at Devasthal, Nainital district, Uttarakhand, is operated by ARIES as a national facility. It was developed by Advanced Mechanical and Optical Systems (AMOS, Belgium) with other international partners, and its technical activation took place in 2016, jointly by the Prime Ministers of India and Belgium.
Source: PIB (Ministry of Communications), 17 December 2025; PIB, 24 June 2025 and 21 December 2024; PIB (Ministry of Science and Technology), 17 March 2025; ARIES, Devasthal Optical Telescope page.
PART 3 — UPSC Integration
Cross-paper relevance
- Prelims (general science) — Image tables for mirrors and lenses, the sign of f and m, R = 2f, refractive-index order (Table 9.3), optical versus mass density, power in dioptres, why rear-view mirrors are convex.
- GS3 (science and technology) — Optical fibre and rural broadband (BharatNet), quantum technologies (National Quantum Mission), observational astronomy (Devasthal Optical Telescope).
Past questions on these themes: Prelims 2026 set a statement question on the National Quantum Mission: its qubit target for intermediate-scale quantum computers and its four thematic hubs. No Mains question in the bank is set directly on this chapter; the closest is GS3 2022 on the James Webb Space Telescope, an adjacent theme.
Frames for Mains Answers
1. Why optical fibre carries the internet. Start from refraction (Class X) and total internal reflection at the core-cladding boundary (Class XII): light stays inside even when the fibre bends, with little loss. Then the policy: ABP's fibre to about 2.64 lakh gram panchayats in a ring topology and to about 3.8 lakh non-GP villages on demand. Close on what fibre makes possible for village services.
2. Light as a quantum technology. NCERT's opening box ends with a quantum theory of light; the National Quantum Mission (2023-24 to 2030-31, ₹6,003.65 crore) builds computing, communication, sensing and materials on that physics through four T-Hubs. State the qubit targets as targets, not results.
3. Instruments built from mirrors and lenses. Concave mirrors concentrate light (headlights, solar furnaces), convex mirrors widen the view (rear-view), and lens powers add in contact (camera, microscope, telescope). India's 3.6-metre Devasthal Optical Telescope shows the same optics at research scale.
Exam Strategy
Prelims fact-traps:
- Object at F of a concave mirror, or at F₁ of a convex lens: the current book says "Image would not be formed"; the 2020-21 tables gave a real, highly enlarged image there.
- Convex mirror and concave lens: always virtual, erect and diminished.
- Mirror: 1/v + 1/u = 1/f and m = −v/u. Lens: 1/v − 1/u = 1/f and m = v/u.
- Negative m means real and inverted, for mirrors and lenses alike.
- f is negative for a concave mirror and a concave lens; positive for a convex mirror and a convex lens.
- R = 2f holds for mirrors of small aperture.
- Kerosene is optically denser than water but lighter.
- Lens powers add only for lenses placed in contact.
- Total internal reflection and the critical angle are Class XII, not Class X.
- BharatNet's ABP covers about 2.64 lakh gram panchayats; non-GP villages are connected on demand.
Mains: Use the chapter as the physics paragraph of a GS3 answer on digital connectivity or quantum technology: one law, one number from NCERT, then the policy facts with their dates.
Practice Questions
Questions 1-6 are the NCERT exercise MCQs. Practice (UPSC-pattern, not past papers): questions 7-10.
1. Which one of the following materials cannot be used to make a lens?
(a) Water
(b) Glass
(c) Plastic
(d) Clay
Answer: (d). Clay is opaque; a lens must be transparent (NCERT Answers, p. 218).
2. The image formed by a concave mirror is observed to be virtual, erect and larger than the object. Where should be the position of the object?
(a) Between the principal focus and the centre of curvature
(b) At the centre of curvature
(c) Beyond the centre of curvature
(d) Between the pole of the mirror and its principal focus
Answer: (d). Last row of Table 9.1 (NCERT Answers, p. 218).
3. Where should an object be placed in front of a convex lens to get a real image of the size of the object?
(a) At the principal focus of the lens
(b) At twice the focal length
(c) At infinity
(d) Between the optical centre of the lens and its principal focus
Answer: (b). Object at 2F₁ gives a same-size image at 2F₂ (NCERT Answers, p. 218).
4. A spherical mirror and a thin spherical lens have each a focal length of –15 cm. The mirror and the lens are likely to be
(a) both concave
(b) both convex
(c) the mirror is concave and the lens is convex
(d) the mirror is convex, but the lens is concave
Answer: (a). Under the sign convention, a negative focal length means a concave mirror and a concave lens (NCERT Answers, p. 218).
5. No matter how far you stand from a mirror, your image appears erect. The mirror is likely to be
(a) only plane
(b) only concave
(c) only convex
(d) either plane or convex
Answer: (d) (NCERT Answers, p. 218).
6. Which of the following lenses would you prefer to use while reading small letters found in a dictionary?
(a) A convex lens of focal length 50 cm
(b) A concave lens of focal length 50 cm
(c) A convex lens of focal length 5 cm
(d) A concave lens of focal length 5 cm
Answer: (c). A convex lens with the page inside its focus gives a virtual, erect, enlarged image; the shorter focal length gives the higher power (NCERT Answers, p. 218). For Exercise 7 (concave mirror, f = 15 cm, erect image) NCERT's key reads "Distance less than 15 cm; virtual; Enlarged."
7. A concave mirror forms a real image of an object. Under NCERT's sign convention, which pair of signs is correct?
(a) v positive, m positive
(b) v negative, m negative
(c) v negative, m positive
(d) v positive, m negative
Answer: (b). A real image of a mirror lies in front of it (against the incident light, so negative) and is inverted (negative m) (pp. 142-143).
8. Consider the following statements, based on NCERT's Table 9.3:
1. Kerosene has a higher refractive index than water.
2. Light travels faster in diamond than in crown glass.
3. A medium that is optically denser always has a higher mass density.
Which of the statements given above is/are correct?
(a) 1 only
(b) 1 and 2 only
(c) 2 and 3 only
(d) 1, 2 and 3
Answer: (a). Kerosene 1.44 > water 1.33. Diamond (2.42) has a higher index than crown glass (1.52), so light is slower in it. Kerosene is optically denser than water but has the lower mass density (p. 149).
9. A lens of power +2.0 D is placed in contact with a lens of power −2.5 D. The combination behaves as
(a) a converging lens of focal length 2 m
(b) a diverging lens of focal length 2 m
(c) a converging lens of focal length 0.5 m
(d) a diverging lens of focal length 0.5 m
Answer: (b). Net power = +2.0 − 2.5 = −0.5 D (algebraic sum, p. 158); f = 1/P = −2 m, and a negative focal length means a concave, diverging combination. (Arithmetic on NCERT's rule.)
10. With reference to the Amended BharatNet Program, consider the following statements:
1. It was approved by the Union Cabinet on 4 August 2023.
2. It provides for optical fibre connectivity to about 2.64 lakh Gram Panchayats in a ring topology.
3. It connects every non-GP village irrespective of demand.
Which of the statements given above is/are correct?
(a) 1 and 2 only
(b) 2 and 3 only
(c) 1 and 3 only
(d) 1, 2 and 3
Answer: (a). Non-GP villages (about 3.8 lakh) are to be connected "on demand basis" (PIB, 17 December 2025; 24 June 2025).
📦 Revision Capsule
Hard Facts
- Laws of reflection hold for all reflecting surfaces; plane-mirror image virtual, erect, same size, laterally inverted.
- R = 2f (small aperture). Concave mirror: real images except with the object between P and F.
- Object at F (concave mirror) or F₁ (convex lens): "Image would not be formed" (Reprint 2026-27).
- Convex mirror and concave lens: always virtual, erect, diminished.
- Mirror 1/v + 1/u = 1/f, m = −v/u; lens 1/v − 1/u = 1/f, m = v/u; P = 1/f, 1 D = 1 m⁻¹.
- sin i / sin r = constant for a given colour and pair of media; n = c/v.
- Table 9.3: air 1.0003, water 1.33, kerosene 1.44, crown glass 1.52, diamond 2.42.
Core Concepts
- One sign convention turns all image positions into one formula per device.
- The sign of m says real or virtual; its size says how much larger or smaller.
- Refraction comes from a change in the speed of light; bending is towards the normal on entering an optically denser medium.
- Power measures how strongly a lens bends light; it adds for lenses in contact.
Confused Pairs
- Optical density vs mass density (kerosene vs water).
- Mirror formula (plus) vs lens formula (minus); m = −v/u vs m = v/u.
- Concave mirror (converging) vs concave lens (diverging).
- "Shifted sideward slightly" (NCERT X) vs "lateral displacement" (guidebook term).
- Refraction (Class X) vs total internal reflection (Class XII).
- Dense flint glass 1.65 (NCERT X) vs 1.62 (NCERT XII).
Data Points
- Speed of light in vacuum 3 × 10⁸ m s⁻¹, marginally less in air.
- Critical angles (Class XII): water 48.75°, crown glass 41.14°, diamond 24.41°.
- ABP: Cabinet 4 Aug 2023; ~2.64 lakh GPs; ~3.8 lakh non-GP villages on demand.
- NQM: Cabinet 19 Apr 2023; ₹6,003.65 crore; 2023-24 to 2030-31; four T-Hubs.
PYQ Pattern
- Prelims 2026: statement question on the National Quantum Mission (qubit target, four thematic hubs).
- No Mains question in the bank matches this chapter directly; GS3 2022 on the James Webb Space Telescope is adjacent.
Sources
- NCERT, Science, Textbook for Class X, ch. 9 "Light – Reflection and Refraction", Reprint 2026-27 — ncert.nic.in PDF.
- NCERT, Science, Class X, Answers, Reprint 2026-27 — ncert.nic.in PDF.
- NCERT, Science, Class X, 2020-21 edition (whole-book zip), as archived on 9 October 2021, ch. 10 "Light – Reflection and Refraction" — Wayback Machine.
- NCERT, Physics Part II, Textbook for Class XII, ch. 9 "Ray Optics and Optical Instruments", Reprint 2025-26 — ncert.nic.in PDF.
- PIB (Ministry of Communications), "Progress under BharatNet", 17 December 2025 — pib.gov.in.
- PIB, "Amended BharatNet Program Operationalises in Gujarat under State-Led Model", 24 June 2025 — pib.gov.in.
- PIB, "BharatNet: Bridging the Digital Divide From Remote Villages to Smart Communities", 21 December 2024 — pib.gov.in.
- PIB (Ministry of Science and Technology), "National Quantum Mission: India's Quantum Leap Unleashing the power of quantum technology and creating jobs of tomorrow", 17 March 2025 — pib.gov.in.
- ARIES (Aryabhatta Research Institute of Observational Sciences), "Devasthal Optical Telescope" — aries.res.in.
