Mirrors and Lenses

1. From plane mirrors to curved mirrors

In Class 7 (chapter "Light: Shadows and Reflections") you met the plane mirror — a flat reflecting surface. Its image is always erect (upright), virtual (cannot be caught on a screen), the same size as the object, and shows lateral inversion (left–right swap, like the word AMBULANCE written backwards on the front of the vehicle).

But hold a shiny steel spoon close to your face: the inner curved side shows your face inverted (upside down), while the bulging outer side shows you erect but smaller. The same spoon gives two completely different images on its two sides. These are curved mirrors, and the most common kind are spherical mirrors — mirrors whose reflecting surface is a part of a sphere.

2. Concave and convex mirrors

A spherical mirror has a curved reflecting surface that can point inward or outward:

• Concave mirror — reflecting surface curves inward (like the inside of a bowl, or the inner side of the spoon). Remember: "concave" = caves in.
• Convex mirror — reflecting surface curves outward (bulges towards you, like the back of the spoon).

In schematic diagrams the non-reflecting (back) surface is shown shaded. To tell them apart by side view: a concave mirror dips in at the middle, a convex mirror bulges up at the middle (NCERT Activity 10.2).

3. Images formed by a concave mirror

This is the trickiest part because the image changes as the object moves. From NCERT Activity 10.3:

• Object placed close to a concave mirror → image is erect and enlarged (bigger than the object).
• Object moved farther away → the image becomes inverted. At first it is still enlarged, then it keeps getting smaller.

So a concave mirror can give an image that is enlarged, diminished, or the same size, and either erect or inverted, depending on the object's distance. This flexibility is why it is so useful (see §6).

4. Images formed by a convex mirror

A convex mirror is far simpler — it has only one behaviour:

As the object is moved away, the image gets only slightly smaller but is always erect and always smaller than the object. Because it shrinks the scene, a convex mirror packs a wide view into a small mirror — it can show a large area behind you.

All three mirror types (plane, concave, convex) show lateral inversion in the image.

5. Comparing the three mirrors

This table is the heart of the chapter — you can identify a mirror just by looking at the image it forms.

6. Where curved mirrors are used

• Concave mirrors (give enlarged/concentrated effects): reflectors in torches, car and scooter headlights; the dentist's mirror (held close to teeth for an enlarged view); the large main mirror of a reflecting telescope; solar concentrators and solar cookers.
• Convex mirrors (give a wide, diminished view): vehicle side-view mirrors; road-safety mirrors at sharp bends and intersections; surveillance mirrors in shops to deter theft.

7. Representing light: rays, incident and reflected rays

We picture light as straight lines with arrows called rays (light travels in a straight line). When a ray hits a mirror:

• Incident ray — the ray that falls on the mirror.
• Reflected ray — the ray that bounces back from the mirror.
• Normal — a line drawn at 90° to the mirror at the exact point where the incident ray strikes (the point of incidence).
• Angle of incidence ($i$) — angle between the incident ray and the normal.
• Angle of reflection ($r$) — angle between the reflected ray and the normal.

Crucial: both angles are measured from the normal, NOT from the mirror surface. This is the single most common source of exam errors.

8. The two laws of reflection

From NCERT Activities 10.4 and 10.5:

The first law was found by measuring angles on paper (Activity 10.4) — $i$ and $r$ always came out equal. The second law was shown (Activity 10.5) by bending the paper holding the reflected beam: when the paper is bent out of the plane, the reflected beam disappears; flatten it and it reappears — proving all three lie in one plane.

Special case: if light falls along the normal (straight onto the mirror), then $i = 0°$, so $r = 0°$ — the light simply bounces straight back.

These laws are valid for ALL mirrors — plane, concave, and convex.

9. Why curved mirrors converge or diverge light

Send several parallel beams at the mirrors (NCERT Activity 10.6):

• Plane mirror → reflected beams stay parallel.
• Concave mirror → reflected beams come closer, i.e. they converge (meet at a point).
• Convex mirror → reflected beams spread out, i.e. they diverge.

Each individual ray still obeys the laws of reflection — it is only the curved shape of the surface that bends the whole beam inward (concave) or outward (convex). Because a concave mirror concentrates light into a small spot, it can focus sunlight to burn paper (Activity 10.7) — the same principle used in solar concentrators to generate heat, steam and electricity.

10. What is a lens?

Place a drop of water over printed text and the letters underneath look bigger (NCERT Activity 10.8) — the rounded water drop is acting like a tiny lens, just like a magnifying glass.

• Convex lens — thicker in the middle than at the edges (bulges out both sides).
• Concave lens — thinner in the middle than at the edges (caves in both sides).

11. Images formed by lenses

From NCERT Activity 10.9, lenses mirror (in behaviour) the two mirror types:

• Convex lens — object close → image erect and enlarged; object moved farther → image becomes inverted, first enlarged then diminished. (Behaves like a concave mirror — can be enlarged/diminished/same, erect or inverted.)
• Concave lens — image is always erect and diminished, wherever the object is. (Behaves like a convex mirror.)

12. Converging and diverging lenses; refraction

Shine parallel beams through the lenses (NCERT Activity 10.10):

• Thin flat glass plate → beam passes through unchanged.
• Convex lens → beam converges (meets at a point) → called a converging lens.
• Concave lens → beam diverges (spreads out) → called a diverging lens.

This bending of light as it passes through a transparent material is called refraction. Because a convex lens converges sunlight, it can burn paper just like a concave mirror (Activity 10.11) — never look at the Sun through a lens or mirror, it can damage your eyes.

13. Where lenses are used

• Eyeglasses / spectacles — to help people see clearly.
• Cameras (including smartphone cameras), telescopes, and microscopes.
• Magnifying glass — a convex lens used to read small print.
• Even the human eye contains a convex lens that changes its shape to let us see near and far objects.

14. NCERT "Keep the curiosity alive" — fully solved

Q1. Incident ray makes 40° with the normal, so $i = 40°$, hence $r = 40°$. The reflected ray makes 40° with the normal, so with the mirror it makes $90° - 40° = $ 50° → option (ii).

Q2. (i) Ray along the normal: $i = 0°$, so $r = 0°$. (ii) Mirror tilted but ray still along the (tilted) normal: again $i = 0°$, $r = 0°$. (iii) Ray at 20° from the normal: $i = 20°$, so $r = 20°$.

Q3. Match images of a sketch-pen cap: (i) same size, erect → plane mirror; (ii) enlarged → concave mirror (object close); (iii) diminished, erect → convex mirror.

Q4. Match images through a transparent piece: (i) unchanged size → flat transparent glass piece; (ii) enlarged → convex lens; (iii) diminished → concave lens.

Q5. Light incident along the normal → (ii) Angle of incidence is 0° (and $r = 0°$ too; reflection still occurs, straight back).

Q6. Image of a graph sheet: plane mirror → squares same size; concave → squares enlarged; convex → squares diminished. Identify each accordingly.

Q7. Woman walking towards a large concave mirror: when far, the image is inverted; as she comes closer it grows, then becomes erect and magnified → (iii).

Q8. A magnifying glass is a convex lens; held close to text it enlarges the letters, but moving it far makes the image inverted and smaller.

Q9. (i) Concave mirror → (a) reflecting surface curves inwards; (ii) Convex mirror → (d) always diminished; (iii) Convex lens → (c) may appear inverted at some distance; (iv) Concave lens → (b) always erect and diminished.

Q10. Assertion (convex mirrors preferred for traffic behind) and Reason (wider view than plane) are both correct and the Reason explains it → (i).

Q11. In O–M–I diagrams, an image larger than the object (a) is a concave mirror; an image smaller (b) is a convex mirror → (iii).

Q12. Pencil behind a tumbler half-filled with water looks bent/magnified due to refraction — light bends as it passes through the curved water surface, which acts like a lens.

15. Common mistakes to avoid

• Measuring $i$ or $r$ from the mirror surface instead of the normal — always measure from the normal.
• Saying a convex mirror "sometimes enlarges" — it is always erect and diminished.
• Mixing up concave (converges, "caves in") and convex (diverges, bulges out).
• Forgetting that a concave mirror gives an enlarged erect image only when the object is close; far objects give an inverted image.
• Thinking lenses "reflect" — lenses let light pass through (refraction), mirrors reflect.
• Forgetting the second law of reflection (same plane) — it carries marks too.

16. Quick revision checklist

• Plane: erect, virtual, same size, laterally inverted.
• Concave mirror: near = enlarged & erect; far = inverted & shrinking. Converges light.
• Convex mirror: always erect & diminished; wide view. Diverges light.
• Laws: $i = r$; incident ray, normal, reflected ray in same plane. Valid for all mirrors.
• Convex lens = converging, thicker middle (like concave mirror behaviour). Concave lens = diverging, thinner middle (like convex mirror).
• Lenses work by refraction; convex lens used in eye, magnifier, camera.