Abhidnya Learning
foundations
Light – Reflection & Refraction
Class X · Chapter 9
Light – Reflection
& Refraction
A complete interactive guide covering concepts, formulas, laws, diagrams and daily-life connections for Class X Physics.
📖 NCERT Based
🔭 Class X Physics
⚡ Quick Revision
🎯 Exam Ready
Core Concepts
FundamentalsWhat is Light?
Light is a form of electromagnetic energy that travels in straight lines (rays) in a homogeneous medium at 3 × 10⁸ m/s in vacuum. It needs no medium to travel — that’s how sunlight reaches us through space!
Reflection of Light
When light hits a surface and bounces back into the same medium, the phenomenon is called reflection.
Daily Life: You see your face in a mirror because of reflection. The still surface of a lake also acts as a mirror!
Did You Know? A mirror doesn’t actually flip left-right — it flips front-to-back! That’s why “LEFT” in a mirror still reads as letters facing you.
Refraction of Light
When light travels from one transparent medium to another, it changes its direction. This bending of light is called refraction.
Daily Life: A pencil partially dipped in water looks bent. Fish in a pond appear closer to the surface than they actually are!
Twinkling Stars: Stars twinkle because their light refracts through layers of moving air in the atmosphere — changing apparent position rapidly!
Spherical Mirrors
Mirrors whose reflecting surface forms part of a sphere. Two types: Concave (inward) and Convex (outward).
Concave 🔵
Converges light · Reflecting side is inward · Used in torches, dental mirrors
Converges light · Reflecting side is inward · Used in torches, dental mirrors
Convex 🟠
Diverges light · Reflecting side is outward · Used in rear-view mirrors
Diverges light · Reflecting side is outward · Used in rear-view mirrors
Why rear-view mirrors are convex: Convex mirrors give a wider field of view but make objects appear smaller — perfect for seeing traffic behind you!
Lenses
Transparent material bound by two surfaces, at least one spherical. Two types: Convex (converging) and Concave (diverging).
Daily Life: Spectacles, magnifying glass, camera, projector, microscope, telescope — all use lenses!
Did You Know? Your eye lens automatically changes shape (accommodation) to focus on near and far objects — just like an auto-focus camera!
Key Mirror Terms
Important geometrical points used in mirror problems.
P – Pole: Midpoint of the mirror surface
C – Centre of Curvature: Centre of the sphere the mirror is part of
R – Radius of Curvature: Radius of that sphere; R = 2f
F – Principal Focus: Point where parallel rays converge/appear to diverge
f – Focal Length: Distance from P to F; f = R/2
Real vs Virtual Image
Two types of images formed by mirrors and lenses.
Real Image
Light rays actually meet · Can be projected on screen · Inverted
Light rays actually meet · Can be projected on screen · Inverted
Virtual Image
Rays appear to meet · Cannot project · Erect · Behind mirror
Rays appear to meet · Cannot project · Erect · Behind mirror
Cinema projector creates a real image on screen. Your bathroom mirror creates a virtual image — you can’t project it!
Laws & Principles
Fundamental RulesLaws of Reflection
1
Same Plane Law
The incident ray, the reflected ray, and the normal at the point of incidence all lie in the same plane.
Like a billiard ball bouncing off the table — all motion stays in one plane.
2
Angle Law
The angle of incidence (∠i) is always equal to the angle of reflection (∠r).
∠i = ∠rTable tennis ball bouncing off the table — it leaves at the same angle it arrived!
Laws of Refraction (Snell’s Law)
1
Coplanar Law
The incident ray, the refracted ray, and the normal at the point of incidence all lie in the same plane.
2
Snell’s Law
For a given pair of media and given colour of light:
where n is the refractive index of the second medium w.r.t. the first.
sin i / sin r = n = constantwhere n is the refractive index of the second medium w.r.t. the first.
Swimmer’s illusion: A pool looks shallower than it is because light bends away from normal coming from water to air — Snell’s Law in action!
New Cartesian Sign Convention
Sign Convention for Spherical Mirrors
All distances measured from Pole P. Distances in direction of incident light → positive; against → negative.
✅ Positive Distances
- Object distance (object on left)
- Image distance (image on right of lens)
- Focal length (convex lens)
- Heights above principal axis
❌ Negative Distances
- Object distance (always −ve for mirrors)
- Focal length of concave mirror, concave lens
- Image distance (real image in mirror)
- Heights below principal axis
🧠 Quick Memory Aid
“LIOD” – Light Incident On Device (mirror/lens) always comes from the left.
Concave mirror & concave lens → negative f
Convex lens → positive f
Concave mirror & concave lens → negative f
Convex lens → positive f
Formulas & Equations
At a Glance🪞 Mirror Formula
1/v + 1/u = 1/f
v image distanceu object distancef focal lengthValid for all spherical mirrors. Apply sign convention carefully!
🔍 Lens Formula
1/v − 1/u = 1/f
v image distanceu object distancef focal lengthNote the minus sign! Unlike the mirror formula, lenses use 1/v − 1/u = 1/f.
📏 Magnification (Mirror)
m = h’/h = −v/u
h' image heighth object heightm<0 real & invertedm>0 virtual & erect📏 Magnification (Lens)
m = h’/h = v/u
h' image heighth object height|m|>1 enlarged|m|<1 diminishedFor lenses: m = v/u (no negative sign, unlike mirrors).
🔵 Focal Length & Radius
f = R / 2
f focal lengthR radius of curvatureThe principal focus lies midway between the pole and centre of curvature.
Solar furnaces use large concave mirrors — the focal point concentrates sunlight to extremely high temperatures!
⚡ Power of a Lens
P = 1/f (in metres)
P power (dioptre, D)f focal length in metres1D = 1 m⁻¹Optician’s prescription like +2.5D means a convex lens with f = 0.4m. Negative power = concave lens.
🌊 Refractive Index
n = c / v = sin i / sin r
n refractive indexc speed in vacuumv speed in mediumi angle of incidencer angle of refraction🔗 Combined Lens Power
P = P₁ + P₂ + P₃ + …
P₁, P₂... individual powersWhen lenses are placed in contact, their powers simply add up — this is why opticians combine lenses!
Spherical Mirrors
Images & UsesConcave Mirror – Ray Diagram (Object beyond C)
Object beyond C → Real, Inverted, Diminished image between C and F
Convex Mirror – Image Formation
Convex mirror ALWAYS gives virtual, erect, diminished image — regardless of object position
Concave Mirror – Image Summary
| Object Position | Image Position | Size | Nature | Daily Use |
|---|---|---|---|---|
| At Infinity | At F | Highly diminished | Real, Inverted | Solar furnace, torch |
| Beyond C | Between F & C | Diminished | Real, Inverted | Solar cooker |
| At C | At C | Same size | Real, Inverted | Terrestrial telescope |
| Between C & F | Beyond C | Enlarged | Real, Inverted | Medical imaging |
| At F | At Infinity | Highly enlarged | Real, Inverted | Searchlights, headlights |
| Between P & F | Behind mirror | Enlarged | Virtual, Erect | Shaving/makeup mirror |
🔵 Concave Mirror Uses
- Torch & car headlights (parallel beam)
- Shaving / make-up mirrors (enlarged image)
- Dental mirrors (large image of tooth)
- Solar cookers & furnaces (concentrate heat)
- ENT doctors & ophthalmologists
🟠 Convex Mirror Uses
- Rear-view mirrors in vehicles (wide field of view)
- Safety/surveillance mirrors in shops
- Street lamp reflectors (diverge light widely)
- ATM security mirrors
A convex mirror in Agra Fort gives a full-length view of the Taj Mahal!
Lenses
RefractionConvex Lens – Converging Action
Parallel rays converge at principal focus F₂ after passing through a convex lens
Concave Lens – Diverging Action
Parallel rays diverge and appear to come from virtual focus F₁ after a concave lens
Convex Lens – Image Summary
| Object Position | Image Position | Size | Nature | Application |
|---|---|---|---|---|
| At Infinity | At F₂ | Highly diminished | Real, Inverted | Camera, telescope objective |
| Beyond 2F₁ | Between F₂ & 2F₂ | Diminished | Real, Inverted | Camera, photocopier |
| At 2F₁ | At 2F₂ | Same size | Real, Inverted | Photocopying (same size) |
| Between F₁ & 2F₁ | Beyond 2F₂ | Enlarged | Real, Inverted | Film projector, enlarger |
| At F₁ | At Infinity | Highly enlarged | Real, Inverted | Searchlights |
| Between F₁ & O | Same side as object | Enlarged | Virtual, Erect | Magnifying glass, reading lens |
Concave Lens – Always the Same!
No matter where the object is placed in front of a concave lens, the image is always Virtual, Erect, and Diminished — between the focus and the optical centre. This is why concave lenses correct myopia (short-sightedness).
Refraction, Dispersion & Scattering
PhenomenaRefractive Index (n)
Ratio of speed of light in vacuum to speed in the medium. A dimensionless quantity always ≥ 1.
n = c/v = sin i / sin r
Diamond (n=2.42) has the highest refractive index among common materials — light slows to less than half its vacuum speed inside a diamond, causing its spectacular sparkle!
Dispersion of Light
Splitting of white light into its constituent colours (VIBGYOR) when passing through a prism. Violet deviates most, Red the least.
Violet (max deviation)Red (min deviation)
Rainbow: Raindrops act like tiny prisms — dispersion + internal reflection inside each droplet creates a rainbow after rain!
Scattering of Light
Deflection of light in all directions by particles in the atmosphere. Shorter wavelengths scatter more (Rayleigh scattering).
Blue sky: Blue light scatters most in the atmosphere (shortest visible wavelength) so the sky appears blue!
Red sunrise/sunset: At sunrise/sunset, sunlight travels a longer path through the atmosphere — blue scatters away leaving only red/orange to reach our eyes.
Tyndall Effect
Scattering of light by colloidal particles, making the beam visible when it passes through a colloidal solution.
Examples: Beam of sunlight through a dusty room, headlight beams visible in fog, light through smoke — all show Tyndall Effect!
Shine a torch through water → invisible. Through milk-water mixture → beam is visible! The colloidal fat particles scatter light (Tyndall Effect).
Atmospheric Refraction
Refraction of light as it passes through Earth’s atmosphere of varying density layers.
Stars twinkle but planets don’t! Planets are close enough to appear as discs — twinkling effects average out. Stars are point sources so even tiny atmospheric shifts change their apparent brightness.
The Sun is visible for ~2 minutes before it actually rises! Atmospheric refraction bends light, showing us the Sun slightly before it’s geometrically above the horizon.
Total Internal Reflection
When light travels from denser to rarer medium at an angle greater than the critical angle, all light is reflected back — no refraction occurs.
Optical fibres use total internal reflection to carry light signals over thousands of kilometres with minimal loss — the backbone of the internet!
Mirages in deserts occur because hot air (less dense) near the ground causes total internal reflection of light from the sky — looks like water!
Refractive Indices of Common Materials
Data, Units & Constants
Reference3 × 10⁸ m/s
Speed of Light (vacuum)
c
1 D = 1 m⁻¹
Unit of Power of Lens
Dioptre (D)
f = R/2
Focal Length Relation
R = radius of curvature
n ≥ 1
Refractive Index Range
Always ≥ 1 for any medium
n(diamond) = 2.42
Highest Common n
Diamond
n(water) = 1.33
Refractive Index of Water
Important for NCERT problems
Quick Symbol Reference
📐 Mirror & Lens Symbols⌄
u – Object distance (always −ve for real objects)
v – Image distance
f – Focal length
R – Radius of curvature = 2f
m – Magnification = h’/h
n – Refractive index = c/v
P – Power of lens = 1/f
h – Height of object
h’ – Height of image
⚡ Key Assumptions⌄
- Mirrors and lenses have small apertures compared to radius of curvature
- Object is always placed to the left of the mirror/lens
- Rays are assumed to be paraxial (close to principal axis)
- Lenses are thin (thickness negligible compared to focal length)
- All distances measured from the pole (mirror) or optical centre (lens)
🎨 Sign Summary at a Glance⌄
Concave Mirror f: Negative
Focus in front → −ve direction
Focus in front → −ve direction
Convex Mirror f: Positive
Focus behind mirror → +ve direction
Focus behind mirror → +ve direction
Convex Lens f: Positive
Real focus on +ve side
Real focus on +ve side
Concave Lens f: Negative
Virtual focus on −ve side
Virtual focus on −ve side
m positive: Virtual, erect image
m negative: Real, inverted image
Quick Quiz
Test Yourself
🎯
Tap an option to check your answer. Explanations appear after each question!
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