Where Mindful Learning Begins
Where Mindful Learning Begins
Class 8 Science Curiosity NCERT Solutions Chapter 10 — every Probe and Ponder prompt, all 11 Activities, all 12 "Keep the Curiosity Alive" exercise questions, and all 3 "Discover, Design, and Debate" project prompts, solved and explained on one page.
This chapter builds up spherical mirrors — concave and convex — and the two laws of reflection, then shows how the same converging and diverging behaviour appears again in convex and concave lenses, ending with everyday uses like torches, side-view mirrors, solar cookers, eyeglasses, and cameras.
Chapter 10 opens with Meena's confusion at a science centre, where curved mirrors made her look enlarged, upside down, or tiny — and uses this to introduce spherical mirrors. It builds up concave mirrors (curved inwards) and convex mirrors (curved outwards), shows how the images they form depend on the object's distance from the mirror, and then establishes the two laws of reflection using a torch, comb, and plane mirror. The same converging/diverging behaviour is then shown to apply to lenses — convex lenses converge light and can enlarge or invert images, while concave lenses always diverge light and form diminished images. The chapter closes with real-world uses: torches, dental mirrors, solar concentrators, side-view mirrors, eyeglasses, and cameras. Every Activity and exercise is solved here exactly as the textbook presents it.
Concave curves inward and converges light; convex curves outward and diverges light — each forms different images.
Angle of incidence equals angle of reflection; the incident ray, normal, and reflected ray all lie in the same plane.
A convex (converging) lens can enlarge or invert an image; a concave (diverging) lens always diminishes it.
Spherical mirrors
A mirror whose reflecting surface is a part of a hollow sphere is a spherical mirror. Spherical mirrors are actually made by grinding and polishing a flat piece of glass into a curved shape, not by slicing a hollow sphere.
| Type | Shape | Effect on parallel rays |
|---|---|---|
| Concave mirror | Reflecting surface curves inwards | Converges (brings together) the rays |
| Convex mirror | Reflecting surface curves outwards | Diverges (spreads out) the rays |
Images formed by mirrors
| Mirror | Object close to mirror | Object far from mirror |
|---|---|---|
| Concave | Erect, enlarged | Inverted; enlarged at first, then diminishes |
| Convex | Erect, diminished | Always erect, diminished (slightly smaller still) |
Two laws of reflection
Both laws of reflection apply to every type of mirror — plane, concave, and convex — even though spherical mirrors additionally converge or diverge multiple parallel rays because of their curved shape.
Uses of mirrors
| Concave mirror | Convex mirror |
|---|---|
| Torch/headlight reflectors, dentist's mirror, solar concentrators, reflecting telescopes | Vehicle side-view mirrors, road-safety mirrors, store surveillance mirrors (wider field of view) |
Lenses
| Type | Shape | Also called | Image |
|---|---|---|---|
| Convex lens | Thicker at the middle than the edges | Converging lens | Erect & enlarged (close); inverted (far) |
| Concave lens | Thicker at the edges than the middle | Diverging lens | Always erect, diminished |
Everyday uses of lenses: eyeglasses, magnifying glasses, cameras, telescopes, microscopes, and even the eye's own natural convex lens.
Sample answer: yes, curved (spherical) mirrors can absolutely give enlarged or diminished images — a concave mirror held close to the face gives an enlarged, erect image (like a shaving or dental mirror), while a convex mirror always gives a diminished, erect image (like a vehicle's side-view mirror).
The side-view mirror warning appears because these mirrors are convex, and a convex mirror always forms an image that is smaller than the actual object. Since the vehicle behind looks smaller than it really is, our brain (which is used to judging distance from apparent size) misjudges it as farther away than it actually is — so the warning reminds drivers that the vehicle is actually closer than the small image suggests.
The curved line seen on some reading glasses usually marks the boundary of a bifocal lens — a lens with two different curvatures (and therefore two different powers) ground into a single piece of glass or plastic, so the wearer can look through the upper part for distance vision and the lower, more curved part for close-up reading, without needing to switch glasses.
This is an open reflection prompt meant to set up the chapter's central ideas — spherical mirrors, laws of reflection, and lenses — all explained in full through the Activities below.
Observation: yes, the shiny spoon acts like a mirror and shows a clear image of the face, but this image looks quite different from the one seen in a flat (plane) mirror.
Inner (concave) surface of the spoon: gives an image that appears inverted (upside down) at typical viewing distance.
Outer (convex) surface of the spoon: gives an image that appears erect (right side up) but smaller in size than the face.
Conclusion: flipping the spoon changes which curved surface faces you, and this changes the type of image formed — the inner curved surface behaves like a concave mirror, while the outer curved (bulging) surface behaves like a convex mirror.
Method: keeping the eye level with the mirrors and looking at them edge-on, the shape of the surface becomes visible in profile.
Observation: the concave mirror's reflecting surface dips downward in the middle, curving inward like the inside of a bowl. The convex mirror's reflecting surface bulges upward in the middle, curving outward like the back of a spoon.
Answer: a mirror whose surface curves inward (dips in the middle when seen from the side) is a concave mirror; one whose surface curves outward (bulges up in the middle) is a convex mirror.
Concave mirror, object close (small distance): the image is erect but larger than the object — enlarged.
Concave mirror, object far (large distance): the image becomes inverted. As the object moves farther, the image is initially enlarged and then gets progressively smaller.
Convex mirror, at any distance: the image is always erect and smaller than the object — diminished. The image gets very slightly smaller still as the object is moved farther away, but it never becomes enlarged or inverted.
Conclusion: unlike a plane mirror, which always gives an erect image of the same size as the object, spherical mirrors (concave and convex) change the size of the image as the object's distance changes, and a concave mirror can even invert the image at larger distances. Lateral inversion (left-right flipping) is seen in images formed by all three types of mirrors.
Method: after marking the mirror's position and drawing the incident ray (the ray falling on the mirror) and reflected ray (the ray bouncing back), a line is drawn at 90° to the mirror at the point where the ray strikes it — this is the normal. The angle between the normal and the incident ray is the angle of incidence (i); the angle between the normal and the reflected ray is the angle of reflection (r).
| S.No. | Angle of incidence (i) | Angle of reflection (r) |
|---|---|---|
| 1 | 20° | 20° |
| 2 | 35° | 35° |
| 3 | 50° | 50° |
Conclusion: if the experiment is done carefully, the recorded angle of incidence and angle of reflection turn out nearly equal in every trial, showing that the angle of incidence is always equal to the angle of reflection — this is the first law of reflection. When the incident beam falls exactly along the normal, both the angle of incidence and the angle of reflection are 0°.
Observation: the reflected beam is clearly visible on the extended flat portion of the sheet. When that portion is bent along the table's edge, the reflected beam disappears from view; flattening the sheet again makes it reappear.
Reason: bending the sheet creates a new, tilted plane that no longer lines up with the plane containing the incident ray and the normal, so the reflected beam (which stays in that original plane) is no longer visible on the bent part.
Conclusion: this shows the second law of reflection — the incident ray, the normal to the mirror at the point of incidence, and the reflected ray all lie in the same plane.
Going further: even when the incident ray strikes the mirror from a different direction, as long as it hits the same point, the normal at that point stays the same, and the reflected ray always adjusts itself so that the incident ray, the normal, and the reflected ray continue to lie together in one plane.
Plane mirror: the multiple reflected beams remain parallel to each other, just like the incident beams.
Concave mirror: the reflected beams bend towards each other and meet — they converge.
Convex mirror: the reflected beams spread apart from each other — they diverge.
Conclusion: even though every individual ray still obeys the laws of reflection at the point it strikes the mirror, the curved shape of a spherical mirror causes a bundle of parallel rays to either converge (concave mirror) or diverge (convex mirror) after reflection — behaviour a flat mirror does not show.
Going further: drawing this out, the plane mirror's reflected rays stay parallel lines; the concave mirror's reflected rays visibly bend inward to cross at a single point; and the convex mirror's reflected rays visibly fan outward as if coming from a point behind the mirror.
Safety first: this activity must always be done under a teacher's or adult's supervision — never look towards the Sun or into the mirror reflecting it, and keep the reflected spot of light aimed only at the paper, never at anyone's face or eyes.
Observation: once the paper is held at just the right distance, a small, very bright, sharp spot of light appears on it. Holding the mirror and paper steady at that distance for a few minutes causes the paper to start smoking and eventually catch fire.
Reason: a concave mirror converges (brings together) the parallel rays of sunlight falling on it into this one small bright spot, concentrating a large amount of light energy — and therefore heat — into a tiny area, enough to ignite the paper.
Going further: devices that concentrate sunlight into a small area using mirrors or lenses are called solar concentrators. The concentrated heat can be used to boil water into steam, which can then generate electricity or provide heat for large-scale cooking or industrial solar furnaces — some solar furnaces are even powerful enough to melt steel.
Shape of the drop: the oil or wax coating stops the water from spreading flat, so the drop settles into a rounded shape with a surface that curves outward, like a tiny dome.
Observation through the drop: the letters of the text directly beneath the water drop appear noticeably larger (magnified) compared to the letters nearby that are seen without the drop.
Reason: the curved, outward-bulging surface of the water drop bends light rays passing through it, making it behave like a simple lens — in this case, one that magnifies. This is the same basic principle behind a magnifying glass.
Convex lens, object close: the image appears erect and enlarged.
Convex lens, object farther away: the image becomes inverted. It is enlarged at first as the distance increases, then it gradually diminishes in size.
Concave lens, at any distance: the image is always erect and diminished (smaller than the object), and its size keeps changing (getting smaller still) as the object's distance from the lens increases — but it never becomes enlarged or inverted.
Conclusion: a convex lens can form enlarged or inverted images depending on the object's distance, while a concave lens always forms an erect, diminished image, regardless of distance.
Thin glass plate: the parallel beam of light passes straight through, unchanged.
Convex lens: the beam bends and converges — the parallel rays meet together after passing through.
Concave lens: the beam bends and diverges — the parallel rays spread apart after passing through.
Conclusion: a convex lens is therefore also called a converging lens, while a concave lens is called a diverging lens.
Going further: drawing this out, rays through the flat glass plate stay parallel straight lines; rays through the convex lens bend inward to cross at a point on the far side; and rays through the concave lens bend outward as if spreading from a point on the near side.
Safety first: never look at the Sun directly or through the lens, as it may damage the eyes.
Answer: yes. Just like a concave mirror, a convex lens converges the parallel rays of sunlight passing through it into a small, sharp, bright spot on the paper. If the paper and lens are held steady at the correct distance for a few minutes, the concentrated light generates enough heat at that spot to make the paper smoke and eventually catch fire.
Takeaway: both concave mirrors (by reflection) and convex lenses (by refraction) can concentrate sunlight to a point and produce enough heat to ignite paper — this is the same converging principle used in solar concentrators.
More than 800 years ago, during the era of the great Indian mathematician and astronomer Bhāskara II, Indian astronomers used shallow bowls of water as improvised mirrors to study the sky. By looking at the reflected images of stars and planets in the still water through tubes held at carefully chosen angles, they were able to measure the positions of these celestial objects with real precision. Although no surviving text from that time explicitly states the laws of reflection the way this chapter does, the accuracy and design of their instruments strongly suggest that these early astronomers had grasped, through practical experience, how a reflecting surface behaves — long before the laws of reflection were written down formally.
Spherical mirrors are not cut out of a hollow glass sphere, even though they can be thought of that way. In practice, they are made by grinding and polishing a flat piece of glass into a curved shape. A reflective coating (such as a thin layer of aluminium) applied to the outer curved surface produces a concave mirror, while applying the same coating to the inner curved surface produces a convex mirror.
Most modern telescopes are reflecting telescopes, and their main mirror — the one responsible for gathering and focusing light from distant objects — is a large concave mirror. This links back to how telescopes were introduced earlier in the "Beyond Earth" chapter of Curiosity, Grade 6.
Answer: (ii) 50°.
Reasoning: by the law of reflection, the angle of reflection (measured from the normal) equals the angle of incidence, so the reflected ray also makes 40° with the normal. Since the normal is drawn at 90° to the mirror's surface, the angle between the reflected ray and the mirror surface itself is 90° − 40° = 50°. It's important to note the question asks for the angle with the mirror, not with the normal.
(i) Ray falls along the normal (mirror not tilted): the ray retraces its own path straight back the way it came. Angle of incidence = 0°, so angle of reflection = 0°.
(ii) Mirror tilted, but ray still falls along the normal to the tilted surface: since the ray is still along the normal (just now tilted along with the mirror), it again reflects straight back along the same line it arrived on. Angle of reflection = 0°.
(iii) Mirror tilted, ray falls at 20° from the normal: the reflected ray leaves on the opposite side of the normal, making an equal angle with it. Angle of reflection = 20°.
Drawing tip: in each case, first draw the normal (a line perpendicular to the mirror's actual surface at the point the ray strikes), then use a protractor to mark the reflected ray at the same angle from the normal as the incident ray, but on the opposite side of the normal.
| Image | Mirror | Why |
|---|---|---|
| (i) | Plane mirror | Reflected cap appears the same size and erect, exactly as a flat mirror always shows |
| (ii) | Concave mirror | Reflected cap appears noticeably enlarged, since the object is close to a concave mirror |
| (iii) | Convex mirror | Reflected cap appears smaller than the actual cap, matching a convex mirror's always-diminished image |
This match is worked out from how each type of mirror is expected to behave (plane: same size; concave: enlarged at close range; convex: always diminished). Since the exact photograph in your printed textbook may show the mirrors in a different left-to-right order, compare the apparent size of the cap's reflection in each photo against this reasoning to confirm the match.
| Image | Lens/glass type | Why |
|---|---|---|
| (i) | Convex lens | Cap's image appears enlarged, matching a convex lens at this distance |
| (ii) | Flat transparent glass piece | Cap's image appears unchanged in size, since flat glass doesn't converge or diverge light |
| (iii) | Concave lens | Cap's image appears diminished, matching a concave lens, which always diminishes |
As with Q3, this match follows directly from each lens's expected effect on image size at a small distance (convex: enlarged; flat glass: unchanged; concave: diminished). Please cross-check against the actual photograph in your textbook, since the left-to-right order of the three images may vary from print to print.
Answer: (ii) Angle of incidence is 0°.
Reasoning: the angle of incidence is measured between the incident ray and the normal. If the incident ray travels exactly along the normal, there is no angle between them, so the angle of incidence — and, by the first law of reflection, the angle of reflection too — is 0°. Reflection still takes place; the ray simply bounces straight back along the same line.
Method: looking at how the grid lines of the reflected graph sheet appear in each mirror reveals the mirror's type — a plane mirror reflects the grid with unchanged spacing (same size), a concave mirror reflects the grid with the squares appearing enlarged (since the graph sheet is close to it), and a convex mirror reflects the grid with the squares appearing smaller and a wider area of the sheet visible at once.
Answer: the mirror showing the grid at its original, unchanged size is the plane mirror; the one showing an enlarged grid is the concave mirror; and the one showing a diminished grid with a wider field of view is the convex mirror.
Since which specific mirror in the photograph shows enlargement versus diminishing depends on the actual image, compare the grid-square sizes in your textbook's Fig. 10.25 against this reasoning to label each mirror correctly.
Answer: (iv) Her erect image keeps increasing in size.
Reasoning: a convex mirror always forms an erect, diminished image, no matter how close or far the object is — it never inverts the image. As she walks towards the mirror (reducing her distance from it), the image she sees of herself remains erect throughout, but it gradually gets larger, since the image's diminished size is closer to her actual size the nearer she is to the mirror.
At a small distance from the text: the letters appear clearly enlarged and erect — this is the distance at which the magnifying glass is normally used for reading small print.
Moving it farther away: the enlargement first increases somewhat, but beyond a certain distance, the image becomes blurred and eventually flips — appearing inverted rather than enlarged and erect.
Answer: a magnifying glass is a convex (converging) lens — the same type of lens studied in Activities 10.9 and 10.10, which is thicker at the middle than at the edges.
| Column I | Matches with (Column II) |
|---|---|
| (i) Concave mirror | (a) Spherical mirror with a reflecting surface that curves inwards |
| (ii) Convex mirror | (b) Forms an image which is always erect and diminished in size |
| (iii) Convex lens | (c) Object placed behind it may appear inverted at some distance |
| (iv) Concave lens | (d) Object placed behind it always appears diminished in size |
Answer: (i) Both Assertion and Reason are correct, and the Reason is the correct explanation for the Assertion.
Reasoning: convex mirrors diverge the light rays falling on them, which lets them capture a much wider field of view than a plane mirror of the same size would — this is exactly why they show a larger area of the road behind, which in turn is exactly why they are preferred for observing traffic behind a vehicle.
Answer: (iv) Figure (a) indicates a plane mirror and Figure (b) indicates a convex mirror.
Reasoning: in both diagrams, the image (I) is shown erect, same orientation as the object (O) — not inverted. A concave mirror only produces an erect image when the object is very close to it, but typically forms an inverted image once the object is farther away, so a diagram showing a consistently erect image at the given object distance rules out concave mirrors in either case. Since a plane mirror always forms an erect image of the same size, and a convex mirror always forms an erect, diminished image, matching Figure (a)'s equal-sized object and image to a plane mirror and Figure (b)'s smaller image to a convex mirror fits the ray diagrams correctly.
Observation: the part of the pencil seen through the water (the lower part, behind the water-filled section of the tumbler) appears to be shifted sideways or "broken" compared to the part seen through the empty (air-filled) upper section of the tumbler — the pencil no longer looks like one continuous straight line.
Reason: light travels at different speeds in air and in water, so a light ray bends (changes direction) as it passes from one medium into the other — a phenomenon called refraction of light. Since light coming from the submerged part of the pencil bends as it exits the water and enters the air (and again as it exits the curved glass), while light from the part above the water travels through air only, our eyes perceive the two portions of the pencil as being displaced relative to each other, making the pencil look bent or broken at the water's surface.
These three prompts are hands-on visits, design projects, and simulation-based explorations rather than fixed-answer questions. Here's guidance on how to approach each one.
Guidance: when visiting, politely ask the doctor or dentist to show and briefly explain the small round mirrors used in ENT and dental instruments. Most of these — including the dentist's mouth mirror and the head mirrors or specula used by ENT specialists — are concave mirrors, because a concave mirror held close to a tooth or the inside of the ear/nose/throat produces an enlarged, erect image, letting the doctor see fine detail in a small, hard-to-view space. Note down the mirror's approximate size and how the doctor angles it to catch and redirect light into the area being examined, and record this as your field observation.
Guidance on the design: a simple and effective design uses a large concave (parabolic-style) reflector — often built cheaply from a wooden or cardboard frame lined with reflective material such as aluminium foil or a mirrored sheet — mounted on an adjustable stand so it can be tilted to track the Sun through the day. Sunlight falling on this curved reflector converges onto a cooking vessel (placed in a dark-coloured pot to absorb heat efficiently) held at the mirror's focus point.
Suggested proposal structure: (1) Objective — reduce reliance on LPG/electricity for daytime cooking; (2) Design — dimensions of the reflector, material (foil-lined cardboard/wood or a metal dish), and the stand/tracking mechanism; (3) Materials list with approximate costs (reflective sheet, frame material, stand, cooking vessel, thermometer for testing); (4) Estimated total budget, kept as low-cost as possible using recycled materials where feasible; (5) Expected benefits — free fuel, no emissions, ideal for sunny days; (6) Safety notes — supervised use only, and care around the concentrated hot spot.
Guidance: a good free simulation to use is a "geometric optics" or "mirrors and lenses" virtual lab (such as those available through PhET Interactive Simulations), where an object can be dragged closer to or farther from a concave/convex mirror or lens while the simulation redraws the resulting image live.
What to record while experimenting: note the object's distance from the mirror/lens each time, and record whether the resulting image is erect or inverted, and enlarged, diminished, or the same size — for both a concave mirror/convex lens (which should show the switch from enlarged-erect to inverted as distance increases, matching Activities 10.3 and 10.9) and a convex mirror/concave lens (which should stay erect and diminished at every distance tested). Comparing the simulation's live ray diagrams with the paper-and-diagram exercises from Activities 10.4 to 10.6 reinforces exactly why each image behaves the way it does.
Now that mirrors, lenses, and reflection are covered, move on to how ancient civilisations tracked time using the sky, revisit Chapter 9 on solutions, or book a free demo class for personalised coaching.
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