Ch 11: Light | Exam Fusion Prep

💡 Light — At a Glance

3×10⁸ m/s

Speed in Vacuum

3900–7800 Å

Visible Wavelength Range

25 cm

Min. Distance of Distinct Vision

Transverse EM

Nature of Light

Light = form of energy; travels in straight line; no medium required
Dual nature — Particle (Newton, Opticks 1704) & Wave (Huygens, 1678)
Photoelectric effect → Einstein (1905) | Planck: energy quantisation (1900); Einstein: light quanta (1905)
Interference → Thomas Young (1801)

📋 Key Formulae

1/v + 1/u = 1/fMirror Formula

1/v − 1/u = 1/fLens Formula

P = 1/f(m) | Unit: DiopterPower of Lens

μ = c / v_mediumRefractive Index

E = hν | P = h/λPhoton Energy & Momentum

90° mirrors → 3 images; 60° mirrors → 5 (symmetric object)Images in Plane Mirror

🪞 Reflection of Light

📘 Definition

Light returns to its original medium after striking a surface (smooth or rough).

Law 1

Angle of Incidence = Angle of Reflection

∠i = ∠rBoth measured from the normal to the surface

Law 2

Coplanarity

Incident ray, reflected ray, and the normal — all three lie in the same plane.

🪟 Classification of Objects (Optical)

Type	Description	Examples
Self-luminous	Produces own light	Sun, Stars, Bulb, Fire
Non-luminous (illuminated by reflected light)	Visible only when light falls on it	Chair, Table, Moon
Transparent	Transmits light sufficiently clearly to see objects through it	Glass, Water, Air
Opaque	Light does not pass through	Metal, Wood, Brick

💡 Dual Nature of Light

Particle Nature

Corpuscular Theory

Proposed by Descartes (1637)
Elaborated by Newton (Opticks, 1704)
Explains: Reflection, Refraction

Wave Nature

Wave Theory

Advocated by Huygens (1678)
Explains: Interference, Diffraction, Polarisation
Light = transverse EM wave

🔮 Plane Mirror

Image: Virtual, Erect, Equal size, Laterally inverted
Image distance = Object distance (behind mirror)

For even integer m = 360°/θ: n = m − 1. Odd/non-integer cases need object-position and geometry conditions. Symmetric cases: 90° → 3; 60° → 5.Number of images formed between two mirrors at angle θ

📘 Uses of Plane Mirror

Solar cooker · Periscope · Kaleidoscope · Regular mirrors

🔵 Spherical Mirrors — Image Table

Concave = Converging mirror | Convex = Diverging mirror

Mirror	Object Position	Image Position	Nature
Concave	At Infinity	At Focus F	Real, inverted, highly diminished
	Beyond C	Between C & F	Real, inverted, diminished
	At C	At C	Real, inverted, same size
	Between C & F	Beyond C	Real, inverted, enlarged
	At F	At Infinity	Real, inverted, highly enlarged
	Between F & P	Behind mirror	Virtual, erect, enlarged
Convex	At Infinity	At F (behind)	Virtual, erect, highly diminished
Convex	Anywhere else	Between F & P	Virtual, erect, diminished

Concave Mirror Uses

Converging Mirror

Shaving mirror · Dentist's mirror · Torch/Headlight · Solar cookers

Convex Mirror Uses

Diverging Mirror

Rear-view mirror (vehicles) · Security mirrors · Blind-corner road mirrors

⚠️ Exam Trap — Mirror Uses

Rear-view mirror = Convex (wide field of view, always virtual diminished image)
Shaving/Dentist mirror = Concave (enlarged virtual image when object between F and P)
Convex mirror always gives virtual, erect, diminished image (for real objects)

📐 Mirror Formulae & Sign Convention

1/v + 1/u = 1/fMirror Formula

f = R/2 | m = −v/u = I/OFocal length & Magnification

📘 Solved Example

Focal length of concave mirror = 10 m
f = R/2 → 10 = R/2 → R = 20 m

Parameter	Convex Mirror	Concave Mirror
Focal length (f)	Positive (+)	Negative (−)
Radius of curvature	Positive (+)	Negative (−)
Object distance (u)	Negative (−)	Negative (−)
Real image distance	N/A	Negative (−)
Virtual image distance	Positive (+)	Positive (+)

🌊 Refraction of Light

📘 Definition

Deviation of the path of light when it enters from one transparent medium into another. Light bends toward the normal when entering a denser medium.

Law 1 — Coplanarity

Incident ray, refracted ray, and the normal all lie in the same plane.

Law 2 — Snell's Law

sin i / sin r = constant (μ)Snell's Law of Refraction

📘 Examples of Refraction

Stars twinkling at night
Pond appears shallower than actual depth
Pencil dipped in water appears bent

📐 Refractive Index

μ = c / v_mediumRefractive index = Speed in vacuum / Speed in medium

Absolute Refractive Index

Refractive index of a medium with respect to vacuum/air.

Relative Refractive Index

Refractive index of second medium with respect to first medium.

⚠️ Exam Trap — Refraction

Higher refractive index = denser medium = light slows down and bends toward normal
Speed of light is reduced in denser medium; frequency remains unchanged
Primary rainbow: refraction and dispersion, one internal reflection, then refraction on exit; the internal reflection is not TIR

💎 Total Internal Reflection (TIR)

📘 Definition

When light travels from denser → rarer medium and angle of incidence exceeds the critical angle, light reflects back into the denser medium entirely.

sin c = n₂/n₁ (n₁ > n₂); into air, sin c ≈ 1/μCritical angle formula | c = critical angle

📘 Conditions for TIR

Light must travel from denser → rarer medium
Angle of incidence must be greater than critical angle

Examples of TIR

Real-World Applications

Shining of a crack in glass
Mirage formation (hot road appears wet)
Optical fibre communication
Shining of air bubble in water
Brilliance of Diamonds (high μ → small critical angle)

⚠️ Exam Trap — TIR

TIR only in denser to rarer medium (NOT rarer to denser)
Diamond sparkles because its critical angle is very small (~24°) → TIR occurs easily
Optical fibres work on TIR — used in internet cables, medical endoscopes
Mirage = TIR due to hot air layers near ground (rarer medium near ground)

🔭 Lenses — Basics

Convex Lens

Converging Lens

Thicker at centre
Converges parallel rays to a focus
Positive focal length
Used for: farsightedness, magnifying glass, camera

Concave Lens

Diverging Lens

Thinner at centre
Diverges parallel rays away from axis
Negative focal length
Used for: shortsightedness (Myopia)

📊 Lens Image Table

Lens	Object Position	Image Position	Nature
Convex	At Infinity	At F₂	Real, inverted, highly diminished
	Beyond C₁	Between F₂ & C₂	Real, inverted, diminished
	At C₁	At C₂	Real, inverted, same size
	Between C₁ & F₁	Beyond C₂	Real, inverted, magnified
	At F₁	At Infinity	Real, inverted, highly magnified
	Between O & F₁	Same side as object	Virtual, erect, magnified
Concave	At Infinity	At F₁	Virtual, erect, highly diminished
Concave	Anywhere else	Between F₁ & O	Virtual, erect, diminished

📐 Lens Formulae

1/v − 1/u = 1/fLens Formula

m = v/u = I/OMagnification

P = 1/f(metres) | Unit: Diopter (D)Power of Lens

📘 Solved Example

f = −20 cm = −0.2 m
P = 1/f = 1/(−0.2) = −5 D (negative = concave lens)

⚠️ Exam Trap — Lens vs Mirror Formula

Mirror: 1/v + 1/u = 1/f (addition)
Lens: 1/v − 1/u = 1/f (subtraction)
Convex lens: P is positive; Concave lens: P is negative
Power unit = Diopter (D) — not metre or Hz

🌈 Dispersion of Light

📘 Dispersion

Splitting of white light into its seven constituent colours when it passes through a prism. Due to different colours having different refractive indices.

Violet · Indigo · Blue · Green · Yellow · Orange · Red

Most Deviated

Violet

Least Deviated

Red

Scatters Most

Violet

Scatters Least

Red

📘 Rainbow

Primary rainbow forms by refraction and dispersion, one internal reflection and refraction on exit from droplets. Sun is behind the observer; the internal reflection is not total.

🎨 Colour Mixing

Green + Red = Yellow

Blue + Red = Magenta

Blue + Green = Cyan

Green + Red + Blue = White

⚠️ Exam Trap — Primary Colours of Light

Primary colours of light: Red, Green, Blue (RGB)
Modern subtractive primaries for pigments/printing: cyan, magenta, yellow (CMY)
Red + Green + Blue light = White
Complementary colours: Red↔Cyan, Green↔Magenta, Blue↔Yellow

🌤️ Scattering of Light

📘 Scattering (Rayleigh Scattering)

Scattering of light after colliding with dust/air particles. Shorter wavelength → more scattering.

Violet scatters the most (shortest wavelength)
Red scatters the least (longest wavelength)
Sky appears blue — blue is scattered more than red/orange (blue has shorter λ than red)
Sun appears red at sunrise/sunset — light travels longer path, blue scattered away, only red reaches eyes
Danger signals are red — red scatters least, visible from long distance

⚠️ Exam Trap — Scattering

Sky appears blue (NOT violet) because human eye is more sensitive to blue than violet. But violet actually scatters MORE than blue.

👁️ Structure of Human Eye

Cornea

Entry path of light; transparent, protruding front part

Iris

Coloured opaque part; controls size of pupil

Pupil

Controls the amount of light entering the eye

Eye Lens

Transparent protein; soft converging lens; adjustable focal length

Retina

Light-sensitive layer; the image formed here is real and inverted

Yellow Spot (Fovea)

Centre of retina; sharpest, clearest vision

Blind Spot

Light sensitivity = zero; image not visible here

Ciliary Muscles

Increase or decrease focal length of eye lens (accommodation)

Choroid Membrane

Black membrane; absorbs stray light

Sclera

Rigid outer membrane; hollow sphere; diameter 25 mm; protective shield

Min. Distinct Vision Distance

25 cm

Normal Vision Range

25 cm to ∞

Power of Human Eye

Approximately 60 D (whole relaxed eye)

👓 Vision Defects & Corrections

Defect	Symptoms / Cause	Correction
Colour Blindness	Difficulty distinguishing certain colours; common inherited form affects red–green discrimination	Inherited form: no cure; acquired cases require evaluation of the cause
Myopia (Short-sightedness)	Distant objects blur; image forms before retina, commonly due to excessive convergence or an elongated eyeball	Concave lens
Hypermetropia (Farsightedness)	Far objects clear, near objects blurred; Curvature of lens reduces	Convex lens
Presbyopia	Age-related loss of accommodation, mainly difficulty focusing near	Reading addition, bifocals or progressive lenses as needed
Astigmatism	Blurred at all distances; irregular curvature of cornea/lens	Cylindrical lens

⚠️ Exam Trap — Vision Defects

Myopia → Concave (diverging) lens
Hypermetropia → Convex (converging) lens
Presbyopia: positive near addition; bifocals/progressives when distance correction is also needed
Common inherited colour deficiency has no cure; acquired colour deficiencies also occur
Astigmatism → Cylindrical lens (not spherical)

🔬 Microscope

Uses convex lens of short focal length
For viewing microscopic objects
Simple microscope (image at near point) magnification: M = 1 + D/F (D = 25 cm, least distance of vision)

🔭 Telescope

Reflecting Telescope

Bright & Magnified Distant Images

Uses a concave mirror as objective. Produces bright images of distant objects.

Astronomical Telescope

For Celestial Bodies

Image at ∞: M = −Fₒ/Fₑ
Image at min. dist: M = −(Fₒ/Fₑ)(1 + Fₑ/D)

⚠️ Exam Trap — Telescope

Objective lens: large focal length (Fₒ)
Eyepiece lens: small focal length (Fₑ)
Higher Fₒ/Fₑ ratio = greater magnifying power

🌊 Interference of Light

📘 Definition

When two waves of equal frequency from coherent sources travel in the same direction, superposition causes alternating bright and dark fringes.

Propounder: Thomas Young (1801)
Constructive interference → bright fringe (max intensity)
Destructive interference → dark fringe (min intensity)
Example: Soap bubble appearing coloured in white light

〰️ Diffraction & Polarisation

Diffraction

Bending of light at sharp edges

Partial bending around obstacles or holes
Fresnel diffraction — nearby point source
Fraunhofer diffraction — parallel rays (source at ∞)

Polarisation

Restricting vibration to one direction

Light vibrations perpendicular to direction of travel
Plane polarised — vibrates in one plane only
Unpolarised — vibrates in all planes
Polarisation proves light is a transverse wave (not longitudinal)

⚛️ Photoelectric Effect & Photon Theory

Photoelectric Effect

Einstein (1905)

When light of sufficient frequency hits a metal, electrons are emitted
Minimum frequency needed = threshold frequency
Proved particle nature of light
Einstein won Nobel Prize (1921) for this

Photon (Quantum) Theory

Planck: energy quantisation (1900); Einstein: light quanta (1905)

Energy emitted/absorbed in discrete bundles = photons

E = hν = hc/λEnergy of photon

P = h/λMomentum of photon

ν = c/λFrequency–wavelength relation

⚠️ Exam Trap — Photoelectric Effect

Einstein explained the photoelectric effect using light quanta in 1905; Planck introduced energy quantisation in 1900
Einstein won Nobel Prize in 1921 for photoelectric effect (not for relativity!)
Maximum photoelectron KE = hν − work function. At fixed frequency and material, intensity changes photoelectron rate, not maximum KE.

🎯 High-Yield Exam Points

Speed of light in vacuum = 3 × 10⁸ m/s
Visible light wavelength = 3900 Å to 7800 Å
Light = Transverse EM wave; no medium needed
Particle nature → Descartes (1637), Newton (Opticks, 1704); Wave → Huygens (1678)
Laws of reflection: ∠i = ∠r; all three in same plane
Plane mirror: image = Virtual, Erect, Equal, Laterally inverted
Rear-view = Convex; Shaving/Dentist = Concave
Mirror formula: 1/v + 1/u = 1/f | f = R/2
Snell's Law: sin i / sin r = constant (μ)
TIR: denser → rarer, angle > critical angle | Applications: Optical fibre, Diamond, Mirage
Lens formula: 1/v − 1/u = 1/f
Power of lens = 1/f(m); unit = Diopter
VIBGYOR: Violet most deviated & most scattered; Red least
Sky = blue (Rayleigh scattering); Sunrise/Sunset = red
Myopia → Concave | Hypermetropia → Convex | Presbyopia → positive near addition; bifocals/progressives if needed | Astigmatism → Cylindrical
Inherited colour deficiency has no cure; acquired deficiencies also occur
Min. distance of distinct vision = 25 cm
Interference: Thomas Young (1801); soap bubble colours
Photoelectric effect: Einstein (1905); Nobel 1921
Planck: energy quantisation (1900); Einstein: light quanta (1905); E = hν

📋 Formula Quick Reference

1/v + 1/u = 1/f | f = R/2Mirror Formula

m = −v/u (mirror) | m = v/u (lens)Magnification

1/v − 1/u = 1/fLens Formula

P = 1/f(m) | Unit: DPower of Lens

μ = c/v | sin c = 1/μRefractive Index & Critical Angle

E = hν | P_photon = h/λPhoton Energy & Momentum

⚠️ Most Common Exam Traps

Mirror formula has +; Lens formula has −
Rear-view = Convex (always virtual, diminished)
Concave mirror: only when between F & P → virtual image
TIR requires denser→rarer medium
Convex lens power = positive; Concave = negative
Colour Blindness: no lens correction
Einstein won Nobel for photoelectric effect, NOT relativity
Sky appears blue (NOT violet — eye sensitivity)
Danger signals = Red (least scattering → visible from far)
Image on retina = Real & Inverted (brain corrects it)

💡 Chapter 11: Light