CBSE Class 10 · Science · board exam 2027
Chapter 9: Light – Reflection and Refraction — notes
The chapter’s 11 parts in the book’s order — the first idea of each and the points Medha Ma’am writes on the board — and the summary at the end. The full lesson and a check question for each part are in the app.
1. Light and the laws of reflection
Because we see an object only when light falling on it is reflected and reaches our eyes.
- • We see an object ⇒ light reflected from it reaches our eyes
- • Ray of light = the straight-line path of light
- • Evidence: a small source casts a sharp shadow of an opaque object
- • A bundle of rays = a beam of light
- • Angle of incidence ∠i = between the incident ray and the normal
- • Angle of reflection ∠r = between the reflected ray and the normal
- • Laws of reflection
- • (i) Angle of incidence = angle of reflection (∠i = ∠r)
- • (ii) The incident ray, the normal and the reflected ray lie in the same plane
- • Plane mirror image
- • virtual and erect, same size (m = 1)
- • as far behind the mirror as the object is in front
- • laterally inverted (left ↔ right)
2. Spherical mirrors and their terms
Take a shining spoon and look at your face in its inner side, then in its outer side.
- • Spherical mirror = reflecting surface that is part of a hollow sphere
- • Concave mirror: reflecting surface curved inwards
- • Convex mirror: reflecting surface curved outwards
- • Pole P = centre of the reflecting surface
- • Centre of curvature C = centre of that sphere
- • Radius of curvature R = PC
- • Principal axis = the line through P and C
- • Principal focus F: parallel rays meet here after reflection (concave)
- • Focal length f = PF
- • Aperture = diameter of the reflecting surface
- • Convex mirror: F and C behind the mirror
- • Reflected rays appear to diverge from F
- • R = 2f ⇒ f = R/2
- • Example: R = 20 cm
- • f = 20/2 cm = 10 cm
- • Activity: image of the Sun by a concave mirror
- • Aim: rough focal length of a concave mirror
- • Materials: concave mirror, white paper, metre scale
- • Method: ① face the mirror to the Sun ② reflected light on the paper ③ move the paper to get a sharp spot
- • Observation: the paper starts burning at the spot
- • Conclusion: the spot is F; mirror-to-paper distance ≈ f
- • Precaution: do not look at the Sun or its reflected light directly
3. Spherical mirrors: the rules of rays
To find where an image forms, we draw at least two rays from the top of the object.
- • Image = where at least two reflected rays meet (or appear to meet)
- • An arrowhead on every ray, to show its direction
- • Rule 1: parallel to the axis ⇒ through F (concave) / appears to come from F (convex)
- • Rule 2: through F (concave) / towards F (convex) ⇒ parallel to the axis
- • Rule 3: through C (concave) / towards C (convex) ⇒ back along the same path
- • Reason: it falls along the normal, ∠i = ∠r = 0°
- • Rule 4: oblique ray at P ⇒ reflected at an equal angle to the axis (∠i = ∠r)
4. Images formed by a concave mirror
A concave mirror has six positions of the object, and the image changes with each one.
- • ① Object at ∞ ⇒ image at F: highly diminished, point-sized, real, inverted
- • ② Object beyond C ⇒ image between F and C: diminished, real, inverted
- • ③ Object at C ⇒ image at C: same size, real, inverted
- • ④ Object between C and F ⇒ image beyond C: enlarged, real, inverted
- • ⑤ Object at F ⇒ image at ∞: highly enlarged, real, inverted
- • ⑥ Object between P and F ⇒ image behind the mirror: enlarged, virtual, erect
- • Outside F: real, inverted | Inside F (between P and F): virtual, erect, enlarged
- • Uses of concave mirrors
- • Torch, searchlight, headlight: bulb at F ⇒ powerful parallel beam
- • Shaving mirror, dentist: between P and F ⇒ large, erect image
- • Solar furnace: sunlight concentrated at F ⇒ heat
5. Images formed by a convex mirror
A convex mirror has only two cases.
- • ① Object at ∞ ⇒ image at F (behind the mirror): point-sized, virtual, erect
- • ② Object between ∞ and P ⇒ image between P and F: diminished, virtual, erect
- • Convex mirror: always diminished, virtual, erect
- • Use: rear-view mirrors of vehicles
- • Reasons: ① image always erect ② wider field of view
6. Sign convention, mirror formula and magnification
We calculate.
- • New Cartesian Sign Convention
- • ① Pole P = origin, principal axis = x-axis
- • ② Object always on the left (light falls from the left)
- • ③ Distances from P: right +, left −
- • ④ Heights: above the axis +, below −
- • So: u always − ; concave mirror f − ; convex mirror f +
- • Mirror formula: 1/v + 1/u = 1/f
- • Put u, v, f with their signs
- • Magnification m = h′/h = −v/u
- • m − ⇒ real, inverted | m + ⇒ virtual, erect
- • |m| > 1 ⇒ enlarged | |m| < 1 ⇒ diminished | |m| = 1 ⇒ same size
- • Example: convex mirror, R = +3.00 m, u = −5.00 m, v = ?
- • Given: R = +3.00 m (C behind ⇒ +), u = −5.00 m (object on the left)
- • f = R/2 = 3.00/2 m = +1.50 m
- • 1/v = 1/f − 1/u
- • 1/v = 1/1.50 − 1/(−5.00) = 1/1.5 + 1/5
- • 1/1.5 + 1/5 = 2/3 + 1/5 = 10/15 + 3/15 = 13/15
- • v = 15/13 m ≈ +1.15 m (+ ⇒ behind the mirror)
- • m = −v/u = −1.15/(−5.00) ≈ +0.23
- • Image: 1.15 m behind the mirror, virtual, erect, diminished
7. Refraction of light
You have seen the bottom of a tank of water look raised, and a pencil partly in water look bent at the surface.
- • Refraction = change in the direction of light going obliquely from one medium into another
- • Examples: raised bottom of a tank, bent pencil, letters raised under a glass slab
- • Reason: the speed of light changes when the medium changes
- • Rarer ⇒ denser: towards the normal (r < i)
- • Denser ⇒ rarer: away from the normal (r > i)
- • Activity: refraction through a glass slab
- • Aim: to observe refraction through a rectangular glass slab
- • Materials: drawing board, white paper, glass slab, pins, protractor
- • Method: ① outline of the slab ② pins E, F on a slanting line ③ pins G, H in line from the other side ④ join to get the path
- • Observation: air ⇒ glass towards the normal; glass ⇒ air away from the normal
- • Conclusion: emergent ray parallel to the incident ray, ∠e = ∠i (lateral displacement)
- • Reason: equal and opposite bending at the two parallel faces
- • Normal incidence (i = 0°) ⇒ the ray goes straight, no bending
- • Laws of refraction
- • (i) Incident ray, refracted ray and normal lie in the same plane
- • (ii) Snell's law: (sin i)/(sin r) = constant (given colour, given pair of media)
- • This constant = refractive index of the second medium with respect to the first, n₂₁
- • n₂₁ = (sin 60°)/(sin 30°)
- • = (√3/2)/(1/2) = √3 ≈ 1.732
8. Refractive index
How much a medium bends light is told by its refractive index.
- • n₂₁ = (speed in medium 1)/(speed in medium 2) = v₁/v₂
- • n₁₂ = v₂/v₁ (the other way round)
- • Absolute refractive index n = c/v
- • c = speed of light in vacuum = 3 × 10⁸ m/s
- • No unit (speed ÷ speed)
- • | Medium | Air | Water | Kerosene | Crown glass | Diamond |
- • | n | 1.0003 | 1.33 | 1.44 | 1.52 | 2.42 |
- • Larger n ⇒ smaller speed of light in that medium
- • Larger n ⇒ optically denser; smaller n ⇒ optically rarer
- • Optical density ≠ mass density
- • Kerosene n = 1.44 > water 1.33 ⇒ kerosene optically denser (but lighter)
- • Given: n = 1.5, c = 3 × 10⁸ m/s
- • v = c/n = (3 × 10⁸)/1.5 m/s
- • 3/1.5 = 2 ⇒ v = 2 × 10⁸ m/s
9. Spherical lenses
Lenses.
- • Lens = transparent material with at least one spherical surface
- • Convex: thicker at the middle ⇒ converging
- • Concave: thinner at the middle ⇒ diverging
- • Two centres of curvature C₁, C₂; principal axis through C₁ and C₂
- • Optical centre O: a ray through O goes straight, without deviation
- • Convex lens: parallel rays meet at F₂ on the other side
- • Two principal foci F₁, F₂; focal length f = OF₂
- • Concave lens: parallel rays diverge, appear to come from F on the same side
10. Images formed by lenses
Lenses also have three easy rays.
- • Rule 1: parallel to the axis ⇒ convex: through F₂; concave: appears to come from F₁
- • Rule 2: through F₁ (convex) / towards F₂ (concave) ⇒ parallel to the axis
- • Rule 3: through O ⇒ straight, no deviation
- • ① At ∞ ⇒ at F₂: point-sized, real, inverted
- • ② Beyond 2F₁ ⇒ between F₂ and 2F₂: diminished, real, inverted
- • ③ At 2F₁ ⇒ at 2F₂: same size, real, inverted (m = −1)
- • ④ Between F₁ and 2F₁ ⇒ beyond 2F₂: enlarged, real, inverted
- • ⑤ At F₁ ⇒ at ∞: highly enlarged, real, inverted
- • ⑥ Between F₁ and O ⇒ same side: enlarged, virtual, erect
- • Use: magnifying glass
- • Concave lens: at ∞ ⇒ at F₁, point-sized; anywhere else ⇒ between F₁ and O: diminished, virtual, erect
11. Lens formula, magnification and power
For a lens all distances are measured from the optical centre O, with the same sign convention.
- • Lens formula: 1/v − 1/u = 1/f
- • Distances from O; convex lens f + , concave lens f −
- • Magnification of a lens m = h′/h = v/u
- • Example: concave lens, f = −15 cm, v = −10 cm, u = ?
- • Given: f = −15 cm (concave), v = −10 cm (image on the object's side)
- • 1/u = 1/v − 1/f
- • 1/u = 1/(−10) − 1/(−15) = −1/10 + 1/15
- • −1/10 + 1/15 = (−3 + 2)/30 = (−1)/30
- • u = −30 cm
- • m = v/u = (−10)/(−30) = 1/3 ≈ +0.33
- • Image: virtual, erect, one-third the size of the object
- • Power of a lens P = 1/f (f in metres)
- • SI unit: dioptre (D); 1 D = 1 m⁻¹
- • Convex lens P + , concave lens P −
- • f = +25 cm = +0.25 m
- • P = 1/0.25 D = +4 D
- • Lenses in contact: P = P₁ + P₂ + P₃ + …
Summary
Very good! Light travels in straight lines, and in reflection the angle of incidence equals the angle of reflection. Spherical mirrors have P, C, F, and R equals 2f. The six cases of a concave mirror, and the always diminished, erect image of a convex mirror. Then refraction, Snell's law, and refractive index n equals c upon v. After that lenses, their ray diagrams, the lens formula one upon v minus one upon u equals one upon f, magnification v upon u, and power P equals one upon f, in dioptres. Draw all of today's ray diagrams once in your notebook, with an arrow on every ray. And write both formulas with their signs without looking. Your homework is on your screen. If anything was not clear, press the Ask button and ask me. Done, you worked very well today!
AskMedha · Medha Ma’am — CBSE Class 10 Science, Chapter 9. Written from the textbook, checked twice.
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