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எல்லைத் தெரிவு செய்து, பகுதி I (MCQ) அல்லது பகுதி II (கட்டுரை) பயிற்சி செய்யுங்கள்.
கேத்திர கணித ஒளியியல் · பகுதி II
அலகு 5 — கேத்திர கணித ஒளியியல்
1. (அ) ஒளியின் தெறிப்பு விதிகளை (laws of reflection) தருக. (3)
(ஆ) சமதள கண்ணாடியில் (plane mirror) உருவாகும் படிமத்தின் 4 பண்புகளை விளக்குக. (4)
(இ) குழி + குவி கண்ணாடிகளின் தினசரி பயன்பாட்டை ஒவ்வொன்றுக்கும் தருக. (3) (10 புள்ளி)
(ஆ) சமதள கண்ணாடியில் (plane mirror) உருவாகும் படிமத்தின் 4 பண்புகளை விளக்குக. (4)
(இ) குழி + குவி கண்ணாடிகளின் தினசரி பயன்பாட்டை ஒவ்வொன்றுக்கும் தருக. (3) (10 புள்ளி)
விடைத் திட்டம்:
- Law 1: i, r, normal same plane.
- Law 2: i = r.
- Plane mirror: virtual, erect, same size, lateral inversion.
- Concave: shaving, headlight, telescope.
- Convex: side mirror, security.
(அ) 2 laws of reflection:
Law 1 — Incident ray, reflected ray, normal (perpendicular at point of incidence) — மூன்றும் ஒரே plane-ல்.
Law 2 — தாக்கல் கோணம் = எதிரொளிப்புக் கோணம் (i = r), both measured from normal.
(ஆ) Plane mirror image — 4 properties:
• Virtual — mirror பின்னால் தோன்றும், screen-ல் project முடியாது.
• Erect — object upright இருந்தால் image-ம் upright.
• Same size — m = 1.
• Lateral inversion — left-right swap. "BUS" → "SUB" appearance.
• Equal distance — object distance = image distance from mirror.
(இ) Concave mirror uses:
• Shaving / dressing mirror (closeup magnification when object < f).
• Vehicle headlight (place bulb at f → parallel beam out).
• Telescope reflector (Newton-style large concave primary).
• Solar furnace / cooker (concentrate sun rays at focus).
Convex mirror uses:
• Vehicle rear-view side mirror (wide angle, virtual smaller image).
• Security mirror at shop / corner.
• Inside elevators, parking garages.
• ATM lobby + corridor blind-spot mirrors.
Law 1 — Incident ray, reflected ray, normal (perpendicular at point of incidence) — மூன்றும் ஒரே plane-ல்.
Law 2 — தாக்கல் கோணம் = எதிரொளிப்புக் கோணம் (i = r), both measured from normal.
(ஆ) Plane mirror image — 4 properties:
• Virtual — mirror பின்னால் தோன்றும், screen-ல் project முடியாது.
• Erect — object upright இருந்தால் image-ம் upright.
• Same size — m = 1.
• Lateral inversion — left-right swap. "BUS" → "SUB" appearance.
• Equal distance — object distance = image distance from mirror.
(இ) Concave mirror uses:
• Shaving / dressing mirror (closeup magnification when object < f).
• Vehicle headlight (place bulb at f → parallel beam out).
• Telescope reflector (Newton-style large concave primary).
• Solar furnace / cooker (concentrate sun rays at focus).
Convex mirror uses:
• Vehicle rear-view side mirror (wide angle, virtual smaller image).
• Security mirror at shop / corner.
• Inside elevators, parking garages.
• ATM lobby + corridor blind-spot mirrors.
2. (அ) ஒளி முறிவு (refraction) என்றால் என்ன? (2) (ஆ) Snell's law சமன்பாட்டை எழுதி, refractive index வரையறையை தருக. (3) (இ) முழு அக எதிரொளிப்பு (TIR) நிபந்தனைகள் + critical angle சமன்பாடு. (3) (ஈ) TIR-ஐ அடிப்படையாகக் கொண்ட 2 முக்கிய பயன்பாடுகளை விளக்குக. (2) (10 புள்ளி)
விடைத் திட்டம்:
- Refraction = light bending across media.
- Snell: n₁sin i = n₂sin r.
- n = c/v.
- TIR: denser → rarer, i > θc.
- sin θc = n₂/n₁.
- Fiber optics + endoscope + diamond brilliance.
(அ) ஒளி முறிவு (Refraction): ஒளி ஒரு medium-இலிருந்து வேறு medium-உக்கு (e.g., air → glass) செல்லும்போது medium-ல் ஒளியின் வேகம் வேறுபடுவதால் — பாதை நேராக நிலையாமல் வளைகின்றது. Air → glass = bend toward normal; glass → air = bend away from normal.
(ஆ) Snell's law:
n₁ sin θ₁ = n₂ sin θ₂
இதில் θ₁ = incident angle (in medium 1), θ₂ = refracted angle (in medium 2).
Refractive index (n): ஒரு medium-ன் optical density அளவீடு.
n = c / v = (Speed of light in vacuum) / (Speed of light in that medium).
Typical values: vacuum 1.00, air ~1.00, water 1.33, glass 1.5, diamond 2.42. Larger n → slower light → more bending.
(இ) முழு அக எதிரொளிப்பு (Total Internal Reflection):
இரண்டு conditions ஒரே நேரத்தில்:
(1) ஒளி denser → less dense medium-உக்கு செல்ல வேண்டும் (e.g., glass → air).
(2) Incident angle i > critical angle θc.
Critical angle equation:
sin θc = n₂ / n₁
Glass-air interface: sin θc = 1 / 1.5 → θc ≈ 42°.
Diamond-air: sin θc = 1/2.42 → θc ≈ 24°.
When i ≥ θc — refracted ray would need sin > 1 (impossible) — ஆகவே refraction நிகழாது, முழு light reflect ஆகும்.
(ஈ) TIR Applications:
• Fiber optics (நார்த்திரள்): Core (high n) + cladding (low n) interface — light TIR செய்து கிலோமீட்டர்கள் travel. Internet backbone, transatlantic submarine cables. Bandwidth + low loss > copper wires.
• Endoscope: Flexible fiber bundle medical instrument. Doctor stomach (gastroscopy), colon, blood vessels-ஐ visualise — invasive surgery தேவையில்லாமல்.
• Diamond brilliance: Diamond θc = 24° low. Cut to maximise internal reflections — light bounces inside multiple times then exits brilliantly. "Fire" of diamonds = engineered TIR + dispersion.
(ஆ) Snell's law:
n₁ sin θ₁ = n₂ sin θ₂
இதில் θ₁ = incident angle (in medium 1), θ₂ = refracted angle (in medium 2).
Refractive index (n): ஒரு medium-ன் optical density அளவீடு.
n = c / v = (Speed of light in vacuum) / (Speed of light in that medium).
Typical values: vacuum 1.00, air ~1.00, water 1.33, glass 1.5, diamond 2.42. Larger n → slower light → more bending.
(இ) முழு அக எதிரொளிப்பு (Total Internal Reflection):
இரண்டு conditions ஒரே நேரத்தில்:
(1) ஒளி denser → less dense medium-உக்கு செல்ல வேண்டும் (e.g., glass → air).
(2) Incident angle i > critical angle θc.
Critical angle equation:
sin θc = n₂ / n₁
Glass-air interface: sin θc = 1 / 1.5 → θc ≈ 42°.
Diamond-air: sin θc = 1/2.42 → θc ≈ 24°.
When i ≥ θc — refracted ray would need sin > 1 (impossible) — ஆகவே refraction நிகழாது, முழு light reflect ஆகும்.
(ஈ) TIR Applications:
• Fiber optics (நார்த்திரள்): Core (high n) + cladding (low n) interface — light TIR செய்து கிலோமீட்டர்கள் travel. Internet backbone, transatlantic submarine cables. Bandwidth + low loss > copper wires.
• Endoscope: Flexible fiber bundle medical instrument. Doctor stomach (gastroscopy), colon, blood vessels-ஐ visualise — invasive surgery தேவையில்லாமல்.
• Diamond brilliance: Diamond θc = 24° low. Cut to maximise internal reflections — light bounces inside multiple times then exits brilliantly. "Fire" of diamonds = engineered TIR + dispersion.
3. (அ) குவி + குழி வில்லைகளின் (lenses) வேறுபாட்டை structure + parallel ray behavior மூலம் விளக்குக. (4)
(ஆ) Lens formula 1/v − 1/u = 1/f பயன்படுத்தி: ஒரு 20 cm focal length convex lens முன்னால் 30 cm-ல் object இருந்தால் image distance + magnification கணக்கிடுக. (4)
(இ) Lens power (dioptre) என்றால் என்ன? +2D + −1D ஆகியவற்றின் focal lengths. (2) (10 புள்ளி)
(ஆ) Lens formula 1/v − 1/u = 1/f பயன்படுத்தி: ஒரு 20 cm focal length convex lens முன்னால் 30 cm-ல் object இருந்தால் image distance + magnification கணக்கிடுக. (4)
(இ) Lens power (dioptre) என்றால் என்ன? +2D + −1D ஆகியவற்றின் focal lengths. (2) (10 புள்ளி)
விடைத் திட்டம்:
- Convex thick center, converges, real images possible.
- Concave thin center, diverges, only virtual.
- u=30, f=20 → v=60, m=2.
- P = 1/f(m). +2D → 0.5m convex; -1D → -1m concave.
(அ) Convex (குவி) vs Concave (குழி) lens:
| பண்பு | Convex | Concave |
|---|---|---|
| Shape | Center thick, edges thin | Center thin, edges thick |
| Parallel rays | Converge at focal point F | Diverge — virtual focal point behind lens |
| Focal length | Positive (+) | Negative (−) |
| Image type | Real or virtual (depends on object position) | Always virtual, erect, reduced |
| Use | Camera, eye, magnifier, hyperopia spectacles | Myopia spectacles, binoculars eyepiece |
(ஆ) Lens calculation:
Given: f = +20 cm (convex), u = −30 cm (object distance, negative by sign convention as object on left of lens; some textbooks use positive — here using lens formula 1/v − 1/u = 1/f with sign convention).
Note — Sri Lankan NIE convention varies; let's use: 1/v − 1/u = 1/f, distances measured from lens, object distance u taken positive on incident side.
For object at 30 cm in front: u = 30 cm.
1/v = 1/f + 1/u (rearranged when object distance positive) — alternatively using 1/f = 1/v − 1/u with u negative:
1/v − 1/(−30) = 1/20
1/v + 1/30 = 1/20
1/v = 1/20 − 1/30 = (3 − 2)/60 = 1/60
v = +60 cm (positive → real image on far side, 60 cm from lens).
Magnification:
m = v/u = 60 / (−30) = −2
Negative sign → inverted image; |m| = 2 → image 2× enlarged.
Image properties: Real, inverted, magnified (2×), at 60 cm behind lens. Used in projectors (slide between f and 2f → enlarged real image).
(இ) Lens Power (Dioptre, D):
P = 1/f(metres). Convex lens P positive; concave negative.
• +2 D convex lens: f = 1/2 = 0.5 m = 50 cm.
• −1 D concave lens: f = −1/1 = −1 m = −100 cm.
Spectacle prescriptions written in dioptres. Right eye +2D / Left eye −1.5D = typical age-related correction.
| பண்பு | Convex | Concave |
|---|---|---|
| Shape | Center thick, edges thin | Center thin, edges thick |
| Parallel rays | Converge at focal point F | Diverge — virtual focal point behind lens |
| Focal length | Positive (+) | Negative (−) |
| Image type | Real or virtual (depends on object position) | Always virtual, erect, reduced |
| Use | Camera, eye, magnifier, hyperopia spectacles | Myopia spectacles, binoculars eyepiece |
(ஆ) Lens calculation:
Given: f = +20 cm (convex), u = −30 cm (object distance, negative by sign convention as object on left of lens; some textbooks use positive — here using lens formula 1/v − 1/u = 1/f with sign convention).
Note — Sri Lankan NIE convention varies; let's use: 1/v − 1/u = 1/f, distances measured from lens, object distance u taken positive on incident side.
For object at 30 cm in front: u = 30 cm.
1/v = 1/f + 1/u (rearranged when object distance positive) — alternatively using 1/f = 1/v − 1/u with u negative:
1/v − 1/(−30) = 1/20
1/v + 1/30 = 1/20
1/v = 1/20 − 1/30 = (3 − 2)/60 = 1/60
v = +60 cm (positive → real image on far side, 60 cm from lens).
Magnification:
m = v/u = 60 / (−30) = −2
Negative sign → inverted image; |m| = 2 → image 2× enlarged.
Image properties: Real, inverted, magnified (2×), at 60 cm behind lens. Used in projectors (slide between f and 2f → enlarged real image).
(இ) Lens Power (Dioptre, D):
P = 1/f(metres). Convex lens P positive; concave negative.
• +2 D convex lens: f = 1/2 = 0.5 m = 50 cm.
• −1 D concave lens: f = −1/1 = −1 m = −100 cm.
Spectacle prescriptions written in dioptres. Right eye +2D / Left eye −1.5D = typical age-related correction.
4. மனிதக் கண் — (அ) 4 முக்கிய பகுதிகளை function-உடன் தருக. (4) (ஆ) Myopia, Hyperopia, Presbyopia, Astigmatism — நான்கின் காரணம் + lens correction. (6) (10 புள்ளி)
விடைத் திட்டம்:
- Cornea — 70% refraction. Iris/pupil — light control. Lens — fine focus. Retina — image plane.
- Myopia: eyeball long → concave lens. Hyperopia: short → convex. Presbyopia: accommodation lost → bifocal. Astigmatism: cornea irregular → cylindrical.
(அ) மனிதக் கண்ணின் முக்கிய பகுதிகள்:
(1) Cornea (கண்சுவர் / பின்னலையம்): பளிங்கு வடிவ வெளி dome. ~70% refraction here (fixed). காற்றில் இருந்து கண்ணுக்குள் ஒளி enter.
(2) Iris (கருவிழி) + Pupil (கருமணி): Iris colored ring; pupil center hole. Iris muscle pupil-ஐ adjust செய்து வரும் ஒளி amount control. Bright → constrict (2 mm); dark → dilate (8 mm).
(3) Lens (கண் வில்லை): Biconvex flexible lens. Ciliary muscles relax/contract → lens shape change → focal length adjust (accommodation). அருகே / தூரம் automatic focus.
(4) Retina (விழித்திரை): Image plane. ~125M rod cells (low light, monochrome) + ~6M cone cells (color, daylight). Fovea = cone-dense central area = sharpest vision. Photo signal → optic nerve → brain visual cortex.
(ஆ) 4 பார்வை குறைபாடுகள்:
(1) Myopia (குறுகியப் பார்வை / short-sight):
காரணம்: Eyeball axial length அதிகம்; image retina-உக்கு முன்னால் focus ஆகின்றது. தூரப் பொருட்கள் blur.
Correction: Concave (diverging) lens — diverges incoming light → effective focal point retinaக்குப் பின்னுக்குச் சென்று focus retina-ல்.
உதா: -2D, -3D spectacles. கணினி, mobile phone work-ஆல் modern epidemic.
(2) Hyperopia / Hypermetropia (தூரப் பார்வை / long-sight):
காரணம்: Eyeball too short; image retina-உக்குப் பின்னால் focus. அருகே blur (writing, reading).
Correction: Convex (converging) lens — converges light → focus moves forward to retina.
உதா: +1D, +2D reading glasses.
(3) Presbyopia (முதிர்வுப் பார்வை):
காரணம்: Age-related — lens hardens, ciliary muscle weakens → accommodation fails. அருகே blur (after 40-45 typically).
Correction: Bifocal / progressive lenses — top portion distance + bottom portion reading.
உதா: அப்பாக்கள் near-blind without specs to read newspaper.
(4) Astigmatism (வளிவு குறை):
காரணம்: Cornea irregular curvature (not perfectly spherical) — horizontal lines + vertical lines focus at different points.
Correction: Cylindrical lens — compensates differential curvature. Often combined with myopia/hyperopia correction.
உதா: மங்கலான வரிகள், reading strain. Common combined prescription.
Modern alternatives: Contact lenses, LASIK surgery (reshape cornea), intraocular lens implant after cataract.
(1) Cornea (கண்சுவர் / பின்னலையம்): பளிங்கு வடிவ வெளி dome. ~70% refraction here (fixed). காற்றில் இருந்து கண்ணுக்குள் ஒளி enter.
(2) Iris (கருவிழி) + Pupil (கருமணி): Iris colored ring; pupil center hole. Iris muscle pupil-ஐ adjust செய்து வரும் ஒளி amount control. Bright → constrict (2 mm); dark → dilate (8 mm).
(3) Lens (கண் வில்லை): Biconvex flexible lens. Ciliary muscles relax/contract → lens shape change → focal length adjust (accommodation). அருகே / தூரம் automatic focus.
(4) Retina (விழித்திரை): Image plane. ~125M rod cells (low light, monochrome) + ~6M cone cells (color, daylight). Fovea = cone-dense central area = sharpest vision. Photo signal → optic nerve → brain visual cortex.
(ஆ) 4 பார்வை குறைபாடுகள்:
(1) Myopia (குறுகியப் பார்வை / short-sight):
காரணம்: Eyeball axial length அதிகம்; image retina-உக்கு முன்னால் focus ஆகின்றது. தூரப் பொருட்கள் blur.
Correction: Concave (diverging) lens — diverges incoming light → effective focal point retinaக்குப் பின்னுக்குச் சென்று focus retina-ல்.
உதா: -2D, -3D spectacles. கணினி, mobile phone work-ஆல் modern epidemic.
(2) Hyperopia / Hypermetropia (தூரப் பார்வை / long-sight):
காரணம்: Eyeball too short; image retina-உக்குப் பின்னால் focus. அருகே blur (writing, reading).
Correction: Convex (converging) lens — converges light → focus moves forward to retina.
உதா: +1D, +2D reading glasses.
(3) Presbyopia (முதிர்வுப் பார்வை):
காரணம்: Age-related — lens hardens, ciliary muscle weakens → accommodation fails. அருகே blur (after 40-45 typically).
Correction: Bifocal / progressive lenses — top portion distance + bottom portion reading.
உதா: அப்பாக்கள் near-blind without specs to read newspaper.
(4) Astigmatism (வளிவு குறை):
காரணம்: Cornea irregular curvature (not perfectly spherical) — horizontal lines + vertical lines focus at different points.
Correction: Cylindrical lens — compensates differential curvature. Often combined with myopia/hyperopia correction.
உதா: மங்கலான வரிகள், reading strain. Common combined prescription.
Modern alternatives: Contact lenses, LASIK surgery (reshape cornea), intraocular lens implant after cataract.
5. Total Internal Reflection-ன் 3 முக்கிய பயன்பாடுகளை — Fiber optics, Endoscope, Diamond brilliance — விரிவாக விளக்குக. ஒவ்வொன்றிலும் physics principle, structure, real-world impact. (10 புள்ளி)
விடைத் திட்டம்:
- Fiber optics: core+cladding, low loss, internet.
- Endoscope: medical visualization.
- Diamond: TIR + dispersion = fire.
(1) Fiber Optics (நார்த்திரள் ஒளியியல்):
Structure: Cylindrical glass core (high refractive index ~1.5) surrounded by cladding (lower n ~1.48). Total diameter — typically 125 μm (hair thickness).
Physics: Light enters at angle < critical angle → travels in straight line inside core. When it hits core-cladding interface — angle > θc (~70°) → TIR. Zigzag propagation through entire fiber, no escape, minimal energy loss.
Real impact:
• Internet: Trans-Atlantic + Trans-Pacific submarine cables fiber-based. Single fiber Tbps capacity.
• Telephone networks: Long-distance calls digitised → fiber → low cost.
• FTTH: Fiber to the home — Sri Lanka now Dialog/SLT rollout.
• Sensors: Strain, temperature, pressure detection (oil pipelines, structural health monitoring).
(2) Endoscope:
Structure: Flexible thin tube with bundle of optical fibers (10,000+). One bundle illuminate (light from outside in) + another bundle imaging fibers (image out). Modern: CCD/CMOS chip at tip + LED.
Physics: Each fiber TIR-carries light. Bundle of ordered fibers preserves spatial mapping → coherent image transmission.
Real impact:
• Gastroscopy: Stomach + esophagus inspection — ulcers, cancer biopsy.
• Colonoscopy: Colon polyps + cancer screening; removal during same procedure.
• Bronchoscopy: Airway inspection (asthma, tumours).
• Arthroscopy: Knee, shoulder joint surgery — minimal invasion.
• Angiography + angioplasty: Heart blood vessel visualisation + stent placement.
• Minimally invasive surgery replaced many open surgeries → faster recovery + smaller scars.
(3) Diamond Brilliance:
Structure: Diamond cut into specific geometry (round brilliant cut = 58 facets — 33 crown + 24 pavilion + culet).
Physics: Diamond n = 2.42 (highest natural material) → θc = 24° very low. Light entering top — pavilion facets reflect via TIR (twice typically) — exits through crown facets toward viewer.
Additional optical effects:
• Dispersion (fire): Different wavelengths different n → colors separate → rainbow flashes.
• Brilliance: Light returning to viewer eye = total internal reflection efficiency.
• Scintillation: Sparkle as diamond/light source moves.
Real impact:
• Jewelry industry: Multi-billion dollar global market driven by TIR-engineered cuts.
• Synthetic diamond (CVD): Same optical properties at lab cost.
• Industrial cutting tools: Hardness + thermal conductivity benefits.
• Optical windows: Diamond high-pressure cells in research.
Structure: Cylindrical glass core (high refractive index ~1.5) surrounded by cladding (lower n ~1.48). Total diameter — typically 125 μm (hair thickness).
Physics: Light enters at angle < critical angle → travels in straight line inside core. When it hits core-cladding interface — angle > θc (~70°) → TIR. Zigzag propagation through entire fiber, no escape, minimal energy loss.
Real impact:
• Internet: Trans-Atlantic + Trans-Pacific submarine cables fiber-based. Single fiber Tbps capacity.
• Telephone networks: Long-distance calls digitised → fiber → low cost.
• FTTH: Fiber to the home — Sri Lanka now Dialog/SLT rollout.
• Sensors: Strain, temperature, pressure detection (oil pipelines, structural health monitoring).
(2) Endoscope:
Structure: Flexible thin tube with bundle of optical fibers (10,000+). One bundle illuminate (light from outside in) + another bundle imaging fibers (image out). Modern: CCD/CMOS chip at tip + LED.
Physics: Each fiber TIR-carries light. Bundle of ordered fibers preserves spatial mapping → coherent image transmission.
Real impact:
• Gastroscopy: Stomach + esophagus inspection — ulcers, cancer biopsy.
• Colonoscopy: Colon polyps + cancer screening; removal during same procedure.
• Bronchoscopy: Airway inspection (asthma, tumours).
• Arthroscopy: Knee, shoulder joint surgery — minimal invasion.
• Angiography + angioplasty: Heart blood vessel visualisation + stent placement.
• Minimally invasive surgery replaced many open surgeries → faster recovery + smaller scars.
(3) Diamond Brilliance:
Structure: Diamond cut into specific geometry (round brilliant cut = 58 facets — 33 crown + 24 pavilion + culet).
Physics: Diamond n = 2.42 (highest natural material) → θc = 24° very low. Light entering top — pavilion facets reflect via TIR (twice typically) — exits through crown facets toward viewer.
Additional optical effects:
• Dispersion (fire): Different wavelengths different n → colors separate → rainbow flashes.
• Brilliance: Light returning to viewer eye = total internal reflection efficiency.
• Scintillation: Sparkle as diamond/light source moves.
Real impact:
• Jewelry industry: Multi-billion dollar global market driven by TIR-engineered cuts.
• Synthetic diamond (CVD): Same optical properties at lab cost.
• Industrial cutting tools: Hardness + thermal conductivity benefits.
• Optical windows: Diamond high-pressure cells in research.
6. Camera, Magnifying glass, Compound Microscope, Astronomical Telescope, Slide Projector — ஐந்து optical instruments-ன் principle + lens configuration + main use-ஐ ஒப்பிட்டுக் காட்டுக. (10 புள்ளி)
விடைத் திட்டம்:
- Camera: single convex lens + sensor.
- Magnifier: single convex, object inside f.
- Microscope: 2 short-f convex.
- Telescope: long-f objective + short-f eyepiece.
- Projector: convex, object 1
Optical Instruments — Comparison Table:
| Instrument | Lens(es) | Object Position | Image Type | Magnification | Use |
|---|---|---|---|---|---|
| Camera | Single convex | Outside 2f | Real, inverted, reduced | M < 1 | Photography |
| Magnifying glass | Single convex | Inside f (between lens + F) | Virtual, erect, enlarged | M > 1 | Reading, hobbies |
| Compound microscope | 2 convex (short-f objective + eyepiece) | Object very close to objective | Final virtual + magnified | 100×–1000× | Cell biology, microbiology |
| Astronomical telescope | Long-f objective + short-f eyepiece | Object at infinity | Virtual, inverted, distant | M = f_obj / f_eye | Astronomy, defense |
| Slide projector | Single convex | Between f and 2f | Real, inverted, magnified | M > 1, large | Lectures, cinema |
Details:
(1) Camera:
Single (or compound) convex lens system. Object > 2f → image between f and 2f. Inverted real image on sensor/film. Phone cameras: complex lens stack + computational photography. Aperture (like iris), shutter speed, sensor sensitivity (ISO) — exposure triangle.
(2) Magnifying glass (Simple magnifier):
Object placed inside focal length. Virtual enlarged image far behind lens. Sherlock Holmes\'s classic tool. Modern variants: jeweler\'s loupe, surgeon\'s magnifier.
(3) Compound microscope:
• Objective lens (short f, near object): Creates real, inverted, magnified intermediate image inside tube.
• Eyepiece (ocular) lens: Acts as magnifier on intermediate image → final virtual magnified image.
• Total mag = M_objective × M_eyepiece. Typically 4× × 10× = 40×; up to 100× × 25× = 2500×.
• Compound microscope cells visible. Bacteria detection. Pathology slides.
(4) Astronomical telescope:
• Objective (large diameter, long focal length): Collects distant light + forms real image of object at focal plane.
• Eyepiece (short f): Magnifies the focal-plane image.
• Mag = f_obj / f_eye. Large objective → high light-gathering + high resolution.
• Optical (Galileo) or reflecting (Newton concave mirror).
• Astronomy: planets, galaxies. Defense: distant observation. Geodesy.
(5) Slide projector:
• Convex projection lens. Object (slide/transparency) placed between f and 2f → image beyond 2f, inverted, real, enlarged.
• Slide inserted upside-down so screen image upright.
• Bright lamp + condenser lens for illumination.
• Modern: digital projectors with DLP/LCD panels — same optics, electronic image source.
| Instrument | Lens(es) | Object Position | Image Type | Magnification | Use |
|---|---|---|---|---|---|
| Camera | Single convex | Outside 2f | Real, inverted, reduced | M < 1 | Photography |
| Magnifying glass | Single convex | Inside f (between lens + F) | Virtual, erect, enlarged | M > 1 | Reading, hobbies |
| Compound microscope | 2 convex (short-f objective + eyepiece) | Object very close to objective | Final virtual + magnified | 100×–1000× | Cell biology, microbiology |
| Astronomical telescope | Long-f objective + short-f eyepiece | Object at infinity | Virtual, inverted, distant | M = f_obj / f_eye | Astronomy, defense |
| Slide projector | Single convex | Between f and 2f | Real, inverted, magnified | M > 1, large | Lectures, cinema |
Details:
(1) Camera:
Single (or compound) convex lens system. Object > 2f → image between f and 2f. Inverted real image on sensor/film. Phone cameras: complex lens stack + computational photography. Aperture (like iris), shutter speed, sensor sensitivity (ISO) — exposure triangle.
(2) Magnifying glass (Simple magnifier):
Object placed inside focal length. Virtual enlarged image far behind lens. Sherlock Holmes\'s classic tool. Modern variants: jeweler\'s loupe, surgeon\'s magnifier.
(3) Compound microscope:
• Objective lens (short f, near object): Creates real, inverted, magnified intermediate image inside tube.
• Eyepiece (ocular) lens: Acts as magnifier on intermediate image → final virtual magnified image.
• Total mag = M_objective × M_eyepiece. Typically 4× × 10× = 40×; up to 100× × 25× = 2500×.
• Compound microscope cells visible. Bacteria detection. Pathology slides.
(4) Astronomical telescope:
• Objective (large diameter, long focal length): Collects distant light + forms real image of object at focal plane.
• Eyepiece (short f): Magnifies the focal-plane image.
• Mag = f_obj / f_eye. Large objective → high light-gathering + high resolution.
• Optical (Galileo) or reflecting (Newton concave mirror).
• Astronomy: planets, galaxies. Defense: distant observation. Geodesy.
(5) Slide projector:
• Convex projection lens. Object (slide/transparency) placed between f and 2f → image beyond 2f, inverted, real, enlarged.
• Slide inserted upside-down so screen image upright.
• Bright lamp + condenser lens for illumination.
• Modern: digital projectors with DLP/LCD panels — same optics, electronic image source.
7. வானவில் (Rainbow) — ஒரு beautiful optical phenomenon. அதன் formation-ஐ refraction, dispersion, total internal reflection ஆகியவற்றோடு step-by-step விளக்கி, primary + secondary rainbow வேறுபாட்டை குறிப்பிடுக. (10 புள்ளி)
விடைத் திட்டம்:
- Sunlight + water droplets.
- Step 1: refraction into droplet.
- Step 2: dispersion — colors separate.
- Step 3: TIR at back of droplet.
- Step 4: refraction out.
- Primary: one TIR, 42° red, 40° violet, red outside.
- Secondary: two TIRs, ~51°, colors reversed, fainter.
Rainbow Formation — 4 step physical process:
A rainbow appears when sunlight encounters water droplets (rain, mist, waterfall spray) at the proper angle relative to the observer.
Step 1 — Refraction (entry):
White sunlight strikes a spherical water droplet. Light enters the droplet at the air-water interface — bends toward normal (denser medium). All wavelengths refract, but slightly different amounts.
Step 2 — Dispersion (color separation):
Refractive index of water depends slightly on wavelength:
• Red light: n ≈ 1.331
• Violet light: n ≈ 1.343
Different n → different bending angles → white light splits into VIBGYOR spectrum. Violet bends most, red least. (Same principle as Newton\'s prism.)
Step 3 — Total Internal Reflection (back wall):
Dispersed light reaches the far side of the droplet (back wall). Strikes water-air interface at angle > critical angle (θc ≈ 48° for water). TIR — light reflects back inside droplet.
Step 4 — Refraction (exit):
Reflected light reaches front of droplet again. Refracts out into air, bending away from normal. Final emission angle ≈ 42° (red) to 40° (violet) from the original incoming sunlight direction.
Geometric result:
• Observer back to sun, droplets in front.
• Light from each droplet emerges at angles 40°-42° from the anti-solar point.
• Each color forms a circle at its specific angle → arcs visible.
• Red on outer edge (42°), violet on inner edge (40°). Spans ~2° of sky.
Primary Rainbow (vivid):
• One internal TIR inside each droplet.
• Light intensity: most light follows this path → bright.
• Color order: Red outside, violet inside.
• Angle: ~42° (red) — 40° (violet).
Secondary Rainbow (faint, outside primary):
• Two internal TIRs inside each droplet.
• Each TIR loses some light → secondary much fainter (~10% intensity).
• Color order REVERSED: Violet outside, red inside.
• Angle: ~51° — wider arc, located outside primary.
• Gap between primary + secondary = "Alexander's dark band" — geometric exclusion zone where no light direction returns.
Observation tips:
• Best seen against dark background (rain cloud).
• Sun must be behind viewer, low in sky (early morning / late afternoon).
• Drizzle / mist gives best rainbows.
• Each viewer sees their own personal rainbow (depends on geometry from observer eye).
Cultural significance: Tamil literature ஐந்து-வண்ண பெரும் வில்; biblical covenant; pot of gold legend (Irish). Real impact: same physics enables optical glory rings (around aircraft shadow) and corona around the moon.
A rainbow appears when sunlight encounters water droplets (rain, mist, waterfall spray) at the proper angle relative to the observer.
Step 1 — Refraction (entry):
White sunlight strikes a spherical water droplet. Light enters the droplet at the air-water interface — bends toward normal (denser medium). All wavelengths refract, but slightly different amounts.
Step 2 — Dispersion (color separation):
Refractive index of water depends slightly on wavelength:
• Red light: n ≈ 1.331
• Violet light: n ≈ 1.343
Different n → different bending angles → white light splits into VIBGYOR spectrum. Violet bends most, red least. (Same principle as Newton\'s prism.)
Step 3 — Total Internal Reflection (back wall):
Dispersed light reaches the far side of the droplet (back wall). Strikes water-air interface at angle > critical angle (θc ≈ 48° for water). TIR — light reflects back inside droplet.
Step 4 — Refraction (exit):
Reflected light reaches front of droplet again. Refracts out into air, bending away from normal. Final emission angle ≈ 42° (red) to 40° (violet) from the original incoming sunlight direction.
Geometric result:
• Observer back to sun, droplets in front.
• Light from each droplet emerges at angles 40°-42° from the anti-solar point.
• Each color forms a circle at its specific angle → arcs visible.
• Red on outer edge (42°), violet on inner edge (40°). Spans ~2° of sky.
Primary Rainbow (vivid):
• One internal TIR inside each droplet.
• Light intensity: most light follows this path → bright.
• Color order: Red outside, violet inside.
• Angle: ~42° (red) — 40° (violet).
Secondary Rainbow (faint, outside primary):
• Two internal TIRs inside each droplet.
• Each TIR loses some light → secondary much fainter (~10% intensity).
• Color order REVERSED: Violet outside, red inside.
• Angle: ~51° — wider arc, located outside primary.
• Gap between primary + secondary = "Alexander's dark band" — geometric exclusion zone where no light direction returns.
Observation tips:
• Best seen against dark background (rain cloud).
• Sun must be behind viewer, low in sky (early morning / late afternoon).
• Drizzle / mist gives best rainbows.
• Each viewer sees their own personal rainbow (depends on geometry from observer eye).
Cultural significance: Tamil literature ஐந்து-வண்ண பெரும் வில்; biblical covenant; pot of gold legend (Irish). Real impact: same physics enables optical glory rings (around aircraft shadow) and corona around the moon.