LIGHT – REFLECTION AND REFRACTION
Class 10 CBSE Science • Easy Language Notes with Diagrams, Tricks & PYQs
ReflectionSpherical MirrorsConcave Mirror
Convex MirrorMirror FormulaSpherical Lens
Lens FormulaPowerRefractionRefractive Index
Glass SlabLaws & SnellNo Bending
1. Reflection of Light
Reflection of light = the bouncing back of light when it hits a polished surface like a mirror.
Laws of Reflection
- Law 1: Angle of incidence = Angle of reflection (∠i = ∠r)
- Law 2: The incident ray, the reflected ray and the normal all lie in the same plane.
Law of reflection: ∠i = ∠r
2. Spherical Mirrors
A spherical mirror is a mirror whose reflecting surface is a part of a hollow sphere.
| Concave Mirror (Converging, “Gufa” – cave) | Convex Mirror (Diverging) |
|---|---|
| Reflecting surface is curved inwards (like inside of a spoon). | Reflecting surface is curved outwards (like back of a spoon). |
| Converges (brings together) parallel rays. | Diverges (spreads out) parallel rays. |
Important Terms
- Pole (P): the middle point (mid-point) of the mirror’s surface.
- Centre of Curvature (C): centre of the hollow sphere of which the mirror is a part.
- Principal Axis (PA): the straight line passing through P and C.
- Radius of Curvature (R): the distance between P and C (radius of the sphere).
Concave mirror: P, F, C, R and f
Principal Focus (F) and Focal Length (f)
- Principal Focus (F): the point on the principal axis where parallel rays meet (concave – actually meet) or appear to come from (convex – behind the mirror).
- Focal Length (f): distance between P and F.
- Concave mirror = Converging mirror • Convex mirror = Diverging mirror
For a spherical mirror: R = 2f (f = R/2)
Image Formation – Basic Ideas
- An image is formed when at least two rays of light meet (or appear to meet).
- If rays actually meet → Real image → always inverted (ulti ↕).
- If rays only appear to meet → Virtual image → always erect (seedhi ↑↑).
3. Image Formation by a Concave Mirror
4 Rules for Ray Diagrams
- A ray parallel to the principal axis → after reflection passes through F.
- A ray passing through F → after reflection becomes parallel to the principal axis.
- A ray passing through C → reflects back along the same path (hits mirror at 90°).
- A ray hitting the pole P → reflects at equal angle on the other side of the axis (∠i = ∠r).
Ray rules (two shown clearly). Rule 2 is the reverse of rule 1.
Position of Object → Image (Concave Mirror)
- Object at infinity (∞): Image at F • Real, inverted, highly diminished (point-sized).
- Object beyond C: Image between C and F • Real, inverted, diminished.
- Object at C special: Image at C • Real, inverted, same size.
- Object between C and F: Image beyond C • Real, inverted, magnified (enlarged).
- Object at F: Image at infinity • Real, inverted, highly magnified.
- Object between F and P very special: Image behind the mirror • Virtual, erect, magnified.
Alakh Sir Concept (ASK): Start with the object at infinity and slowly move it towards the mirror. The image moves from F → away towards ∞ (always real, inverted). As soon as the object crosses F (goes between F and P), the image jumps behind the mirror and becomes erect and magnified. Remember: only ONE case (between F & P) gives an erect image.
Summary Table – Concave Mirror
| Position of Object | Position of Image | Size of Image | Nature of 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 | Highly enlarged | Real and inverted |
| Between P and F | Behind the mirror | Enlarged | Virtual and erect |
Uses of Concave Mirror
- Car headlights and torches – bulb is placed at F so a strong parallel beam comes out.
- Dentist’s mirror – gives an erect, magnified image of teeth (tooth kept between P and F).
- Shaving mirror – gives an erect, enlarged image of the face (face between P and F).
- Solar furnace – sun is at infinity, so rays are focused at F to produce heat.
PYQs – Concave Mirror
CBSE 2025An object is placed 30 cm from a concave mirror of radius of curvature 40 cm. The image formed is: (A) Virtual and magnified (B) Virtual and diminished (C) Real and magnified (D) Real and diminished
R = 40 cm → f = R/2 = 20 cm. Object at 30 cm lies between F (20) and C (40) → image beyond C, real, inverted, enlarged. Answer: (C) Real and magnified.
CBSE 2023A student wants an erect image using a concave mirror of 10 cm focal length. Distance of object from mirror?
Erect image only when object is between F and P → distance less than 10 cm. Answer: (A).
CBSE Term 2021-22Image is the same size as object, f = 15 cm. Distance between the object and its image?
Same size → object at C (30 cm) and image also at C. Both are at the same place, so distance = Zero. Answer: (D).
CBSE 2024Three concave mirrors: A (f = 20 cm, object 45 cm), B (f = 15 cm, object 30 cm), C (f = 30 cm, object 20 cm).
Step 1: C = 2f → A: 40 cm, B: 30 cm, C: 60 cm.
a) Case 1 (mirror A) – object (45) is beyond C (40) → image between C and F, diminished.
b) Case 2 – object at C → image at C: real, inverted (and same size).
c) Mirror C – object (20 cm) is between F (30) and P → image is behind the mirror, virtual, erect and magnified.
a) Case 1 (mirror A) – object (45) is beyond C (40) → image between C and F, diminished.
b) Case 2 – object at C → image at C: real, inverted (and same size).
c) Mirror C – object (20 cm) is between F (30) and P → image is behind the mirror, virtual, erect and magnified.
4. Image Formation by a Convex Mirror
4 Rules for Ray Diagrams
- A ray parallel to the principal axis → after reflection appears to come from F (behind mirror).
- A ray directed towards F → after reflection goes parallel to the principal axis.
- A ray directed towards C → reflects back along the same path.
- A ray hitting the pole P → reflects at an equal angle (∠i = ∠r).
Image Formation
Convex mirror = “seedhi + choti image” (erect + small).
- Object at finite distance (anywhere except ∞): Image between P and F (behind the mirror) • Virtual, erect (upright), diminished.
- Object at infinity (∞): Image at F • Virtual, erect, highly diminished (point-sized).
| Position of Object | Position of Image | Size of Image | Nature of Image |
|---|---|---|---|
| At infinity | At the focus F | Highly diminished, point-sized | Virtual and erect |
| Between infinity and pole P | Between P and F | Diminished | Virtual and erect |
Use of Convex Mirror
🚙 Rear-view mirror in vehicles. Reasons: (1) it always gives an upright (erect) image, (2) it gives a wider field of view (you can see more traffic behind).
Summary – Concave vs Convex Mirror
| Concave Mirror | Convex Mirror |
|---|---|
| Can form inverted (real) images and erect / upright, enlarged images (seedhi + badi, when object between F and P). | Only erect and virtual image. Always diminished (seedhi + choti). |
CBSE 2025List four properties of the images formed by convex mirrors when objects are placed anywhere in front of their reflecting surfaces.
1) Virtual 2) Erect (upright) 3) Diminished 4) Formed on the other side of the mirror w.r.t. object (behind the mirror, between F and P).
5. Sign Convention, Mirror Formula & Magnification
New Cartesian Sign Convention
- All distances are measured from the Pole (P) of the mirror.
- Distances measured along the direction of incident light (to the right, +x axis) are positive (+); distances against it (to the left, –x axis) are negative (–).
- Heights above the principal axis are positive (+h); heights below the axis are negative (–h).
Mirror Formula
1/f = 1/v + 1/u
f = focal length • u = object distance • v = image distance
Notes: (1) u is always negative (object is always in front of mirror). (2) Convex mirror → f is +ve; Concave mirror → f is –ve.
Notes: (1) u is always negative (object is always in front of mirror). (2) Convex mirror → f is +ve; Concave mirror → f is –ve.
Magnification (m)
m = hᵢ / hₒ and m = –v / u
hᵢ = height of image, hₒ = height of object, u = object distance, v = image distance.
m is +ve → virtual & erect • m is –ve → real & inverted • |m| > 1 → magnified • |m| < 1 → diminished.
m is +ve → virtual & erect • m is –ve → real & inverted • |m| > 1 → magnified • |m| < 1 → diminished.
Magnification and Nature of Image
| m | hᵢ | Meaning |
|---|---|---|
| m = 2 | hᵢ = 2 × hₒ | Erect, twice as big |
| m = 1/2 | hᵢ = ½ hₒ | Erect, half the size |
| m = –2 | hᵢ = –2 × hₒ | Inverted, twice as big |
| m = –1/2 | hᵢ = –½ hₒ | Inverted, half the size |
Solved Numericals – Mirrors (PYQs)
CBSE 2025Object 10 cm in front of a concave mirror of focal length 15 cm. Find the image position.
u = –10 cm, f = –15 cm
1/v = 1/f – 1/u = –1/15 + 1/10 = (–2 + 3)/30 = 1/30
v = +30 cm (image is 30 cm behind the mirror – virtual, erect, magnified).
1/v = 1/f – 1/u = –1/15 + 1/10 = (–2 + 3)/30 = 1/30
v = +30 cm (image is 30 cm behind the mirror – virtual, erect, magnified).
CBSE 2024Object 18 cm from the pole of a concave mirror of focal length 12 cm. Find image position.
u = –18 cm, f = –12 cm
1/v = –1/12 + 1/18 = (–3 + 2)/36 = –1/36
v = –36 cm (image is 36 cm in front of the mirror – real and inverted).
1/v = –1/12 + 1/18 = (–3 + 2)/36 = –1/36
v = –36 cm (image is 36 cm in front of the mirror – real and inverted).
CBSE 2025Object 30 cm from a concave mirror; real, inverted image at 60 cm in front. Focal length?
u = –30, v = –60
1/f = 1/v + 1/u = –1/60 – 1/30 = –3/60 = –1/20 → f = –20 cm. Answer: (B).
1/f = 1/v + 1/u = –1/60 – 1/30 = –3/60 = –1/20 → f = –20 cm. Answer: (B).
CBSE 2025Convex rear-view mirror, f = 1.5 m. A 3 m high bus is 6.0 m away. Find position and size of image.
f = +1.5 m, u = –6 m, hₒ = 3 m
1/v = 1/f – 1/u = 2/3 + 1/6 = 5/6 → v = 6/5 = +1.2 m (behind mirror)
m = –v/u = –1.2/–6 = +1/5 = 0.2
hᵢ = m × hₒ = 0.2 × 3 = 0.6 m (erect, diminished).
1/v = 1/f – 1/u = 2/3 + 1/6 = 5/6 → v = 6/5 = +1.2 m (behind mirror)
m = –v/u = –1.2/–6 = +1/5 = 0.2
hᵢ = m × hₒ = 0.2 × 3 = 0.6 m (erect, diminished).
CBSE 2024(Convex mirror ray diagram) Complete the ray diagram; state nature, position, size; sign of image distance.
Nature: erect, virtual • Position: between F and P (behind mirror) • Size: diminished • Image distance (v) is positive (+ve) since the image is behind the mirror.
CBSE 2024“Linear magnification produced by a spherical mirror is +3.”
a) Concave mirror (only concave can magnify). b) Object between F and P. c) Two other properties: virtual, erect (and formed behind the mirror). Also hᵢ = 3 × hₒ.
6. Spherical Lens
| Convex Lens | Concave Lens |
|---|---|
| Thick in the middle, thin at edges | Thin in the middle, thick at edges |
| Converging lens | Diverging lens |
- Optical Centre (O): the central point of the lens. A ray passing through O goes undeviated (straight).
- Principal Axis: line passing through O joining the centres of curvature.
- Principal Focus (F): every lens has two foci – F₁ and F₂ because it has two curved surfaces. 2F₁ and 2F₂ are twice the focal length.
- Focal length (f): distance between O and F.
Principal Focus Behaviour
- Convex lens: parallel rays converge and meet at F₂ (on the other side).
- Concave lens: parallel rays diverge; they appear to come from F₁ (on the same side as the object).
Rules for Ray Diagram – Convex Lens
- A ray parallel to the principal axis → after refraction passes through F₂.
- A ray passing through the optical centre O → goes straight without bending.
- A ray passing through F₁ → after refraction becomes parallel to the principal axis.
Image Formation by Convex Lens
- Object at ∞: Image at F₂ • Real, inverted, highly diminished (point-sized).
- Object beyond 2F₁: Image between F₂ and 2F₂ • Real, inverted, diminished.
- Object at 2F₁: Image at 2F₂ • Real, inverted, same size.
- Object between 2F₁ and F₁: Image beyond 2F₂ • Real, inverted, magnified.
- Object at F₁: Image at infinity • Real, inverted, highly magnified.
- Object between F₁ and O: Image on the same side as the object • Virtual, erect, magnified.
ASK Concept (convex lens): Move the object from ∞ towards the lens. The image moves from F₂ to ∞ on the other side and stays real and inverted. When the object is between F₁ and O, the image flips to virtual, erect and magnified on the same side.
Summary Table – Convex Lens
| Position of Object | Position of Image | Relative Size | Nature |
|---|---|---|---|
| At infinity | At focus F₂ | Highly diminished, point-sized | Real and inverted |
| Beyond 2F₁ | Between F₂ and 2F₂ | Diminished | Real and inverted |
| At 2F₁ | At 2F₂ | Same size | Real and inverted |
| Between F₁ and 2F₁ | Beyond 2F₂ | Enlarged | Real and inverted |
| At focus F₁ | At infinity | Infinitely large / highly enlarged | Real and inverted |
| Between F₁ and O | Same side of lens as object | Enlarged | Virtual and erect |
CBSE 2024At what distance from a convex lens should an object be placed to get an image of the same size on a screen?
Same size → object at 2F₁ = twice the focal length. Answer: (C).
CBSE 2023Object placed beyond 2F of a convex lens – nature of image?
Real, inverted and diminished. Answer: (A).
Concave Lens – Rules
- A ray parallel to the principal axis → after refraction it diverges, appearing to come from F₁.
- A ray passing through the optical centre O → goes straight, undeviated.
Image Formation by Concave Lens
- Object at finite distance (anywhere except ∞): Image between F₁ and O • Virtual, erect, diminished.
- Object at ∞: Image at F₁ • Virtual, erect, highly diminished (point-sized).
| Position of Object | Position of Image | Relative Size | Nature |
|---|---|---|---|
| At infinity | At focus F₁ | Highly diminished, point-sized | Virtual and erect |
| Between infinity and optical centre O | Between F₁ and O | Diminished | Virtual and erect |
Summary – Convex vs Concave Lens
| Convex Lens | Concave Lens |
|---|---|
| Can form inverted (real) images and also erect, magnified image (object between F₁ and O). | Always erect/upright and diminished (seedhi + choti image). |
7. Sign Convention, Lens Formula & Magnification
- All distances are measured from the optical centre (O) of the lens (pole → optical centre).
- All other sign rules are the same as for mirrors. (u → –ve, convex lens f → +ve, concave lens f → –ve.)
1/f = 1/v – 1/u
m = hᵢ/hₒ = v/u
Mirror formula: 1/f = 1/v + 1/u | Lens formula: 1/f = 1/v – 1/u. Mirror m = –v/u, Lens m = +v/u. Real image on a screen → m is negative.
Solved Numericals – Lenses (PYQs)
CBSE 2025Object height 4.0 cm at 30 cm from a convex lens of focal length 20 cm. Find (a) image distance (b) image height.
f = +20, u = –30, hₒ = 4
1/v = 1/f + 1/u = 1/20 – 1/30 = (3 – 2)/60 = 1/60 → v = +60 cm
m = v/u = 60/–30 = –2 → hᵢ = m × hₒ = –2 × 4 = –8 cm (real, inverted, magnified).
1/v = 1/f + 1/u = 1/20 – 1/30 = (3 – 2)/60 = 1/60 → v = +60 cm
m = v/u = 60/–30 = –2 → hᵢ = m × hₒ = –2 × 4 = –8 cm (real, inverted, magnified).
CBSE 2025Magnification for a lens is –2. Object is 20 cm from the optical centre. State (i) nature (ii) size compared to object (iii) position of image (iv) sign of height of image.
m = v/u → –2 = v/(–20) → v = +40 cm (other side of lens)
(i) Real, inverted, magnified (ii) Twice the size of object (hᵢ = –2hₒ) (iii) 40 cm from O on the other side (iv) Negative (–ve).
(i) Real, inverted, magnified (ii) Twice the size of object (hᵢ = –2hₒ) (iii) 40 cm from O on the other side (iv) Negative (–ve).
CBSE Term 2021-22Image of a candle flame on a screen is 3 times the size of the flame. The lens is:
(A) Concave, m = +3 (B) Concave, m = –3 (C) Convex, m = –3 (D) Convex, m = +3
Image on a screen → real, inverted → m is negative → m = –3, and only a convex lens forms real images. Answer: (C).
8. Power of a Lens
The power (P) of a lens is its ability to converge or diverge rays of light. It is defined as the reciprocal of its focal length.
P = 1 / f (f in metres)
- SI unit = Dioptre (D). f (in m) = f (in cm) / 100
- Convex lens → f +ve → P positive (e.g. +2 D, +5 D) → converging.
- Concave lens → f –ve → P negative → diverging.
Power of Combination
P = P₁ + P₂ + P₃ + … = 1/f₁ + 1/f₂ + 1/f₃ + …
CBSE 2023Object 1 m from a lens of power +2 D. (i) Type of lens (ii) focal length and image distance.
(i) P positive → convex (converging) lens.
(ii) f = 1/P = 1/2 m = 0.5 m = 50 cm.
u = –1 m: 1/v = 1/f + 1/u = 2 – 1 = 1 → v = +1 m (100 cm, on the other side).
(ii) f = 1/P = 1/2 m = 0.5 m = 50 cm.
u = –1 m: 1/v = 1/f + 1/u = 2 – 1 = 1 → v = +1 m (100 cm, on the other side).
CBSE Term 2021-22Power of a combination of two lenses is +1.0 D. Focal length of one lens is +20 cm. Focal length of the other?
P₁ = 100/20 = +5 D. P = P₁ + P₂ → 1 = 5 + P₂ → P₂ = –4 D → f₂ = –1/4 m = –25 cm. Answer: (C).
CBSE 2025 – HomeworkObject 20 cm from a concave lens; image on the same side at 10 cm. Find (i) focal length (ii) power.
u = –20, v = –10
1/f = 1/v – 1/u = –1/10 + 1/20 = –1/20 → f = –20 cm
P = 1/f = 1/(–0.2) = –5 D.
1/f = 1/v – 1/u = –1/10 + 1/20 = –1/20 → f = –20 cm
P = 1/f = 1/(–0.2) = –5 D.
9. Refraction of Light
Refraction = the bending of a light ray when it travels from one medium to another.
Cause: Light travels with different speeds in different media.
Cause: Light travels with different speeds in different media.
- Rarer → Denser: light slows down and bends TOWARDS the normal.
- Denser → Rarer: light speeds up and bends AWAY from the normal.
- Denser medium = the medium in which the speed of light is less.
10. Refractive Index
Absolute Refractive Index (R.I.)
nₓ = c / vₓ
c = speed of light in air/vacuum = 3 × 10⁸ m/s • vₓ = speed of light in medium X.
Water: nw = c / vw • Glass: ng = c / vg
Water: nw = c / vw • Glass: ng = c / vg
n ∝ 1/v → higher n means lower speed = optically denser medium. Example: nA = 2, nB = 5 → B is denser, speed of light is less in B.
Relative Refractive Index
n₂₁ = n₂ / n₁ = v₁ / v₂
R.I. of medium 2 with respect to medium 1. Similarly, R.I. of A w.r.t. B: nAB = nA / nB = vB / vA.
CBSE 2023Absolute refractive indices of water and glass are 4/3 and 3/2. In which medium is the speed of light more?
nw = 4/3 ≈ 1.33 (rarer) and ng = 3/2 = 1.5 (denser). Smaller n → greater speed. Speed of light is more in water.
CBSE 2025Absolute R.I. of X and Y are 6/5 and 4/3. R.I. of Y with respect to X?
nYX = nY/nX = (4/3) ÷ (6/5) = (4/3) × (5/6) = 20/18 = 10/9. Answer: (A).
11. Refraction Through a Glass Slab
- At the first surface (air → glass): ray bends towards the normal.
- At the second surface (glass → air): ray bends away from the normal.
- The emergent ray is parallel to the incident ray (provided the medium on both sides is the same).
- ∠e = ∠i (angle of emergence = angle of incidence).
- The emergent ray is only shifted sideways (lateral displacement), not changed in direction.
Emergent ray is parallel to the incident ray, ∠e = ∠i
12. Laws of Refraction & Snell’s Law
- The incident ray, the normal and the refracted ray all lie in the same plane.
- The ratio of sine of angle of incidence to sine of angle of refraction is constant for a given pair of media (Snell’s Law).
sin i / sin r = constant = n₂₁
For different angles in the same pair of media: sin i₁ / sin r₁ = sin i₂ / sin r₂ = sin i₃ / sin r₃ = n₂₁ = constant. The constant is the refractive index of medium 2 w.r.t. medium 1.
13. Cases of No Bending (No Refraction)
- Normal incidence: when the ray falls along the normal (perpendicular to the surface), ∠i = 0° and ∠r = 0° → the ray goes straight without bending.
- No change in medium (or no change in refractive index) → no refraction, light keeps going straight.
Quick Revision
Concave mirror: f –ve • Convex mirror: f +ve • Convex lens: f +ve • Concave lens: f –ve
Mirror: 1/f = 1/v + 1/u, m = –v/u | Lens: 1/f = 1/v – 1/u, m = v/u | P = 1/f (m) | n = c/v | n₂₁ = n₂/n₁
Concave mirror: f –ve • Convex mirror: f +ve • Convex lens: f +ve • Concave lens: f –ve
Mirror: 1/f = 1/v + 1/u, m = –v/u | Lens: 1/f = 1/v – 1/u, m = v/u | P = 1/f (m) | n = c/v | n₂₁ = n₂/n₁