Chapter 9 of 13

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Rajasthan (RBSE)Class 10 Science★ 6–8 marks · RBSE Class 10 Science board (Unit — Physics)

Light – Reflection and Refraction

RBSE Class 10 Science Chapter 9 — reflection at spherical mirrors and refraction through lenses. Covers image formation, the mirror and lens formulas, magnification, the sign convention, refractive index and Snell's law, and power of a lens, with ray-diagram tips and fully solved numericals.

⏱ 34 min readHard difficulty✓ Free · NCERT-aligned

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By the end of this chapter you'll be able to…

1Draw ray diagrams for spherical mirrors and lenses
2Apply the mirror and lens formulas with the sign convention
3Calculate magnification and interpret its sign
4Use refractive index and Snell's law
5Calculate the power of a lens and combine lenses

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Why this chapter matters

The heaviest physics chapter of Class 10 — it reliably carries a ray diagram, a mirror/lens numerical and several MCQs. Mastery of the sign convention converts these into secure marks.

Light – Reflection and Refraction — RBSE Class 10 (Science)

A spoon shows you upside-down on one side and upright on the other; a straw looks bent in a glass of water; a magnifying glass gathers sunlight to a burning point. Light bends and bounces by exact rules, and once you know them you can predict every image — its position, size and nature. This is the most formula-and-diagram-driven chapter in Class 10 physics.

1. Reflection at spherical mirrors

A concave mirror curves inward (converging); a convex mirror curves outward (diverging). Key terms: pole (P), centre of curvature (C), focus (F), radius R and focal length f, with $f = \frac{R}{2} .$

Rules for ray diagrams (concave/convex):

A ray parallel to the axis passes through (or appears from) F.
A ray through F becomes parallel to the axis.
A ray through C returns along itself.

Concave images change with object position (real/inverted, or virtual/erect when the object is between P and F). A convex mirror always gives a virtual, erect, diminished image → wide field of view (vehicle rear-view mirrors).

2. The mirror formula, magnification and sign convention

$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}, m = \frac{h ^{'}}{h} = - \frac{v}{u}$

New Cartesian sign convention: distances measured from the pole; along the incident-light direction are +, opposite are −. Heights above the axis +, below −. Consequences: concave $f$ is −, convex $f$ is +. A negative m means a real, inverted image; positive m a virtual, erect image.

3. Refraction of light

Light bends when it passes between media of different optical density. Going into a denser medium it bends towards the normal; into a rarer medium, away from the normal.

Snell's law: $\frac{sin i}{sin r} = n_{21}$ (a constant). The refractive index of a medium is $n = \frac{speed of light in vacuum c}{speed in the medium v} .$ A higher $n$ means light travels slower and bends more (e.g. diamond $n \approx 2.42$ ).

4. Refraction through lenses

A convex (converging) lens is thick in the middle; a concave (diverging) lens is thin in the middle. Terms: optical centre O, principal focus F, focal length f.

Rules for ray diagrams:

A ray parallel to the axis passes through F (convex) / appears from F (concave).
A ray through O goes straight, undeviated.
A ray through F emerges parallel to the axis.

A convex lens gives real images for distant objects and a magnified virtual image when the object is within f (a magnifying glass). A concave lens always gives a virtual, erect, diminished image.

5. Lens formula, magnification and power

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}, m = \frac{h ^{'}}{h} = \frac{v}{u}$

The power of a lens measures its converging/diverging ability: $P = \frac{1}{f ( in metres )} (unit: dioptre, D) .$ Convex lens power is +, concave −. For lenses in contact, powers add: $P = P_{1} + P_{2}$ .

6. Worked idea

An object is 10 cm in front of a concave mirror of focal length 15 cm. Where is the image? Sign convention: $u = - 10$ , $f = - 15$ . $\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = - \frac{1}{15} + \frac{1}{10} = \frac{1}{30}$ , so $v = + 30$ cm — a virtual, erect, magnified image behind the mirror ( $m = - v / u = + 3$ ).

7. Closing thought

Two formula-pairs (mirror & lens) plus a strict sign convention solve every numerical; three ray rules draw every image. Learn concave-mirror image cases, remember convex mirror/concave lens always give small virtual images, and treat power in dioptres. In the RBSE board this chapter is a heavyweight — expect a ray diagram, a numerical, and MCQs worth 6–8 marks.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Focal length

f = R/2

For spherical mirrors.

Mirror formula

1/v + 1/u = 1/f

New Cartesian sign convention.

Lens formula

1/v − 1/u = 1/f

Note the minus sign (vs mirror).

Magnification

mirror m = −v/u; lens m = v/u

m = h'/h; sign gives image nature.

Refractive index

n = c/v = sin i / sin r

Higher n → slower light, more bending.

Power of lens

P = 1/f(m); unit dioptre; P = P₁ + P₂

Convex +, concave −.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Ignoring the sign convention

✓ Apply the New Cartesian convention: u is negative for real objects, concave f negative, convex f positive. Plug signs in before solving.

WATCH OUT

✗ Using the mirror formula for a lens

✓ Mirror: 1/v + 1/u = 1/f. Lens: 1/v − 1/u = 1/f. The sign of the u-term differs.

WATCH OUT

✗ Confusing the two magnification formulas

✓ Mirror m = −v/u; lens m = v/u. Do not swap them.

WATCH OUT

✗ Wrong image nature from m

✓ Negative m → real, inverted image; positive m → virtual, erect image.

WATCH OUT

✗ Power in cm instead of metres

✓ P = 1/f with f in METRES. f = 20 cm = 0.2 m → P = +5 D.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Intext questions

Mirrors, refraction, lenses and numericals

Questions

Ex s

Exercises

Ray diagrams, formula problems, power of lens

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Concept

Which mirror is used as a vehicle rear-view mirror and why?

▶ Show solution

Step 1 — A convex mirror; it always gives an erect, diminished image with a wide field of view.

✦ Answer: convex mirror, for a wider view.

Q2EASY· Focal length

A concave mirror has radius of curvature 30 cm. Find its focal length.

▶ Show solution

Step 1 — f = R/2 = 30/2 = 15 cm (negative by convention: −15 cm).

✦ Answer: 15 cm (f = −15 cm).

Q3EASY· Power

Find the power of a convex lens of focal length 25 cm.

▶ Show solution

Step 1 — f = 0.25 m; P = 1/0.25 = +4 D.

✦ Answer: +4 D.

Q4MEDIUM· Refractive index

The speed of light in a medium is 2 × 10⁸ m/s. Find its refractive index (c = 3 × 10⁸ m/s).

▶ Show solution

Step 1 — n = c/v = (3×10⁸)/(2×10⁸).

Step 2 — n = 1.5.

✦ Answer: 1.5.

Q5MEDIUM· Mirror numerical

An object is placed 20 cm from a concave mirror of focal length 10 cm. Find the image distance.

▶ Show solution

Step 1 — u = −20, f = −10. 1/v = 1/f − 1/u = −1/10 + 1/20 = −1/20.

Step 2 — v = −20 cm (real, in front of the mirror).

✦ Answer: v = −20 cm.

Q6MEDIUM· Lens numerical

A convex lens of focal length 10 cm forms an image of an object placed 15 cm away. Find v and the magnification.

▶ Show solution

Step 1 — u = −15, f = +10. 1/v = 1/f + 1/u = 1/10 − 1/15 = 1/30.

Step 2 — v = +30 cm (real image on the other side).

Step 3 — m = v/u = 30/(−15) = −2 (real, inverted, magnified twice).

✦ Answer: v = 30 cm, m = −2.

Q7HARD· Sign convention

An object is 10 cm from a concave mirror of focal length 15 cm. Find the image position and nature.

▶ Show solution

Step 1 — u = −10, f = −15. 1/v = 1/f − 1/u = −1/15 + 1/10 = 1/30.

Step 2 — v = +30 cm (behind the mirror ⇒ virtual).

Step 3 — m = −v/u = −30/(−10) = +3 (erect, magnified 3×).

✦ Answer: virtual, erect, magnified image 30 cm behind the mirror.

Q8HARD· Combining lenses

Two lenses of powers +5 D and −2 D are placed in contact. Find the power and focal length of the combination.

▶ Show solution

Step 1 — P = P₁ + P₂ = 5 + (−2) = +3 D.

Step 2 — f = 1/P = 1/3 m ≈ 33.3 cm (converging).

✦ Answer: +3 D, f ≈ 33.3 cm.

Q9HARD· Convex mirror

An object is 15 cm from a convex mirror of focal length 10 cm. Find the image distance.

▶ Show solution

Step 1 — u = −15, f = +10. 1/v = 1/f − 1/u = 1/10 + 1/15 = 1/6.

Step 2 — v = +6 cm (virtual, behind the mirror).

✦ Answer: v = +6 cm (virtual, erect, diminished).

Q10MEDIUM· Ray diagram

State the nature of the image when an object is placed between the pole and focus of a concave mirror.

▶ Show solution

Step 1 — The image is virtual and erect.

Step 2 — It is enlarged and forms behind the mirror.

✦ Answer: virtual, erect and magnified (behind the mirror).

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•f = R/2 for spherical mirrors.
•Mirror: 1/v + 1/u = 1/f, m = −v/u.
•Lens: 1/v − 1/u = 1/f, m = v/u.
•Sign convention: real object u negative; concave f −, convex f +.
•Convex mirror and concave lens always give virtual, erect, diminished images.
•n = c/v = sin i/sin r (Snell's law).
•Power P = 1/f(m) in dioptres; powers add in contact.

Rajasthan (RBSE) marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 6–8 marks

Question type	Marks each	Typical count	What it tests
MCQ / very short	1	2	Mirror/lens types, focal length, power
Short answer	2	1	Refractive index; simple numerical
Long answer / numerical / diagram	3	1–2	Mirror/lens numerical or ray diagram

Prep strategy

Master the sign convention before attempting numericals
Practise ray diagrams for all concave-mirror object positions
Keep the mirror (+) and lens (−) formulas distinct
Always convert f to metres for power in dioptres

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Spectacles

Convex and concave lenses correct long- and short-sightedness (power in dioptres).

Vehicle mirrors

Convex mirrors give drivers a wide rear view.

Cameras and microscopes

Lens combinations form sharp, magnified images.

Solar concentrators

Concave mirrors and convex lenses focus sunlight to a point.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Write down u, v, f with correct signs before substituting.
Choose the right formula (mirror vs lens) and matching magnification.
Interpret the sign of v and m to state image nature.
Draw at least two standard rays for image construction.
Convert focal length to metres for any power calculation.

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Total internal reflection and critical angle.
Lens maker's formula and combinations of thin lenses.
Spherical and chromatic aberration.
Deviation through a prism and dispersion.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

RBSE Class 10 Board (BSER Ajmer)High — a ray diagram and a numerical almost every year

NTSE / state scholarshipMedium — optics MCQs

JEE / NEET FoundationHigh — ray optics is core physics

Science Olympiad (NSO)Medium — optics numericals

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Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

Yes — RBSE (BSER, Ajmer) prescribes the NCERT Science textbook, so the chapters and formulas match the national syllabus while RBSE sets its own exam pattern.

A negative m indicates a real, inverted image; a positive m indicates a virtual, erect image. Its size (|m|) tells you enlargement or diminution.

It changes speed. Entering a denser medium it slows and bends towards the normal; entering a rarer medium it speeds up and bends away from the normal.

P = 1/f with f in metres, measured in dioptres (D). A convex lens has positive power, a concave lens negative; powers of lenses in contact add.

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