Physics
🔒 Log in to trackLight — mirrors, lenses, eye, dispersion and scattering
🔒 Log in to trackBasics
- Speed of light in vacuum c ≈ 3 × 10⁸ m/s; slower in water and glass. Refractive index n = c / v.
- Diamond has a very high refractive index (about 2.42) → small critical angle → sparkles by total internal reflection.
Mirrors
| Mirror | Image nature | Uses |
|---|---|---|
| Plane | Virtual, erect, same size, laterally inverted | Looking glass, periscope |
| Concave (converging) | Real/inverted or virtual/enlarged | Shaving/make-up mirror, dentist's mirror, torch & headlight reflector, solar furnace |
| Convex (diverging) | Always virtual, erect, diminished; wide field of view | Rear-view mirror of vehicles, street corners |
Lenses and the eye
| Defect | Cause | Correction |
|---|---|---|
| Myopia (short-sightedness) | Image forms in front of retina | Concave lens |
| Hypermetropia (long-sightedness) | Image forms behind retina | Convex lens |
| Presbyopia | Ageing, weak ciliary muscles | Bifocal lens |
| Astigmatism | Uneven cornea curvature | Cylindrical lens |
- Power P = 1/f (f in metres), unit dioptre; convex lens +, concave lens −.
- Normal eye: near point 25 cm, far point infinity. Rods — dim light; cones — colour. Image on the retina is real and inverted.
- Persistence of vision (about 1/16 s) makes cinema possible.
Refraction phenomena
- A pencil looks bent in water; a pool looks shallower than it is.
- Twinkling of stars — atmospheric refraction (planets do not twinkle much as they are nearer, extended sources).
- Sun is visible about 2 minutes before actual sunrise and after actual sunset.
- Total internal reflection: optical fibres, mirage, sparkle of diamond. Needs light going from denser to rarer medium beyond the critical angle.
Dispersion and scattering
- White light splits into VIBGYOR through a prism (Newton); violet deviates most, red least. A rainbow forms by refraction, dispersion and internal reflection in raindrops and is seen opposite the Sun.
- Scattering is stronger for shorter wavelengths (Rayleigh) → the sky is blue; the Sun looks red at sunrise/sunset (long path); danger signals are red (least scattered, seen from far). The sky looks black to astronauts in space (no atmosphere to scatter).
- Raman effect — C.V. Raman, discovered 28 Feb 1928 (National Science Day), Nobel Prize 1930.
- Primary colours of light: Red, Green, Blue; R + G = yellow, G + B = cyan, R + B = magenta; all three = white.
Light — the basics
Light is a form of energy that makes things visible; in one medium it moves in straight lines (that is why shadows form). Its speed in vacuum is c ≈ 3 × 10⁸ m/s — the highest speed in the universe; in water or glass it slows down. Refractive index n = c / v, so in glass (n ≈ 1.5) light moves at about 2 × 10⁸ m/s. Sunlight takes about 8 minutes 20 seconds to reach the Earth.
Mirrors — which one for which job
| Mirror | Image | Standard uses |
|---|---|---|
| Plane | Virtual, erect, same size, laterally inverted | Looking glass, periscope (two mirrors at 45°) |
| Concave (converging) | Real inverted when the object is far; magnified virtual image when close | Shaving and make-up mirrors, dentist's mirror, torch/headlight/searchlight reflectors, solar furnaces |
| Convex (diverging) | Always virtual, erect, diminished; wide field of view | Rear-view mirrors of vehicles, mirrors at dangerous road bends |
| A concave mirror brings parallel rays to a focus, so it collects the Sun's heat (solar furnace) or sends lamp light out as a beam (headlight). A convex mirror shows a wide, upright view of the traffic behind. |
Lenses — converging and diverging
A convex lens (thicker in the middle) converges rays: it is the lens of a magnifying glass, camera, projector, microscope and telescope objective, and of the eye itself. Object within F → magnified, erect, virtual image (magnifier); object beyond 2F → real, inverted, diminished image (camera). A concave lens always forms a virtual, erect, diminished image of a real object; it corrects short sight. Power P = 1/f with f in metres; unit dioptre (D). Convex power is positive, concave negative. Lenses in contact: powers simply add.
The eye and its defects
The eye's lens forms a real, inverted image on the retina; the brain reads it upright. The nearest clear-vision distance is about 25 cm; the far point is at infinity. Rods see in dim light, cones sense colour. About 1/16 s of persistence of vision makes cinema possible.
| Defect | What goes wrong | Correction |
|---|---|---|
| Myopia (short-sightedness) | Distant objects blur — image forms in front of the retina (eyeball too long) | Concave (diverging) lens |
| Hypermetropia (long-sightedness) | Near objects blur — image forms behind the retina (eyeball too short) | Convex (converging) lens |
| Presbyopia | Old age — lens loses flexibility | Bifocal lens (concave top, convex bottom) |
| Astigmatism | Uneven curvature of the cornea | Cylindrical lens |
| Cataract | Lens turns opaque | Surgery; artificial lens implanted |
| Colour blindness is not a lens problem — the retinal cones lack some colour sensors — so no lens can correct it; red–green confusion is the common type. |
Refraction and total internal reflection
When light passes obliquely between transparent media, it bends (refraction) because its speed changes: towards the normal entering a denser medium, away in a rarer one. Effects: a pencil in water looks bent, a pool looks shallower, stars twinkle (shifting atmospheric refraction; planets hardly twinkle), and the Sun is visible about 2 minutes before actual sunrise and after actual sunset. When light inside a denser medium hits the boundary with a rarer one beyond the critical angle, it is completely reflected back — total internal reflection (TIR). This gives the sparkle of a diamond, carries calls through optical fibres, guides the endoscope, and creates the mirage in deserts.
Dispersion and scattering — why the world is coloured
White light is a mixture of seven colours (VIBGYOR). A prism splits it (dispersion) because each colour bends differently: violet most, red least. Newton proved this by recombining the colours with a second prism. A rainbow is nature's prism: sunlight dispersed and totally internally reflected inside raindrops, seen with the Sun behind the observer; in the primary rainbow red is on the outside. Scattering by tiny air molecules is strongest for short wavelengths (about 1/λ⁴). So the sky looks blue, the Sun looks red at sunrise and sunset (blue is scattered away en route), and danger signals are red (least scattered, visible farthest). A red rose in green light looks almost black: it reflects only red.
Question types you will see
Each type: how to recognise it, the method step by step, and one question to try.
Mirror ↔ image/use matching
'Which mirror is used as a rear-view / shaving / dentist's mirror?', 'what type of image does a convex mirror always form', properties of a plane-mirror image.
Job decides the mirror: wide upright view → convex; enlarged close view or beaming light → concave.
Convex mirror always gives virtual, erect, diminished images.
Plane mirror: virtual, erect, same size, laterally inverted, image as far behind as the object is in front.
A dentist's mirror is a —
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Concave mirror. Held close to the tooth (inside the focus) it gives an erect, magnified image.
Lens ↔ image/use matching
'Which lens is used in a magnifier/camera/projector?', 'a concave lens always forms …', 'which lens converges light'.
Converging = convex lens: magnifier, camera, projector, eye lens.
Diverging = concave lens: always virtual–erect–diminished for real objects; corrects myopia.
Magnifier condition: object inside the focal length → erect magnified virtual image.
A camera lens produces an image that is —
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Real, inverted and diminished. The object is far beyond 2F, so the image lands between F and 2F, close to F.
Eye defects and their correction
A defect (myopia, hypermetropia, presbyopia, astigmatism, cataract, colour blindness) and its cause or corrective lens.
Short-sighted = myopia → concave lens; long-sighted = hypermetropia → convex lens ('My-Con, Hyper-Vex').
Old-age near+far both faulty → bifocal; uneven cornea → cylindrical; cloudy lens → cataract surgery.
Colour blindness has no lens correction — reject any lens option.
Presbyopia of old age is corrected by —
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Bifocal lenses — a convex lower part for reading and a concave upper part for distance.
Power of a lens and light-speed numericals
Focal length given, power asked (or reverse), lenses in contact; or distance ÷ speed-of-light time.
Convert the focal length to metres first: 25 cm = 0.25 m.
P = 1/f; convex +, concave −. For several thin lenses in contact, add the powers.
Light questions: t = distance ÷ (3 × 10⁸ m/s).
dioptre is defined as inverse metres, so the metre conversion is the only trap.
Two thin lenses of powers +2 D and −0.5 D are placed in contact. Find the power and nature of the combination.
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P = 2 + (−0.5) = +1.5 D — converging, since the net power is positive.
Refraction and total internal reflection effects
A phenomenon (bent pencil, shallow pool, twinkling stars, early sunrise, mirage, optical fibre, diamond sparkle) and its cause.
Object looks bent/displaced/shallow, stars twinkle, Sun rises early → refraction.
Light stays inside (diamond sparkle, optical fibre, endoscope) or a mirage → total internal reflection.
Refraction happens because light changes speed between media; TIR needs denser → rarer beyond the critical angle.
Why do stars twinkle but planets hardly do?
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Starlight refracts through constantly shifting layers of the atmosphere, so its brightness flickers. Planets are much closer and act as extended sources, so the changes average out.
Dispersion, scattering and colour facts
Why the sky is blue, why danger signals are red, prism/VIBGYOR order, which colour bends most, rainbow facts, object colour in coloured light.
Sky blue / sunset red / danger red → scattering (blue scatters most, red least).
Prism splits white light: violet bends most, red least (VIBGYOR from bottom to top).
Rainbow: dispersion + TIR in raindrops, Sun behind the observer, red on the outer edge of the primary bow.
A body shows the colour it reflects; it looks black in light it fully absorbs.
A red rose is seen in green light. What colour does it appear?
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Almost black — the rose reflects only red light and absorbs green.
Formula sheet
unit dioptre
Cartesian sign convention
f = R/2
c = 3 × 10⁸ m/s
Shortcuts that save time
Myopia → Concave; Hypermetropia → convex. Short-sighted people cannot see far — a diverging lens pushes the image back onto the retina.
A person who cannot see distant objects clearly needs which lens?
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A concave (diverging) lens — the defect is myopia.
Need a wide view → convex (vehicle rear view). Need an enlarged or focused image/beam → concave (shaving, dentist, headlight).
Mistakes to avoid
Where most students lose marks on this subtopic.
Explaining the blue sky by reflection or refraction — it is scattering.
Saying red deviates most in a prism — violet deviates most, red least.
Choosing a concave mirror for rear-view — vehicles use convex mirrors.
Quick revision
Read this the night before the exam.
c = 3 × 10⁸ m/s; n = c/v; sunlight ≈ 8 min 20 s.
Plane: lateral inversion. Concave mirror: shaving, dentist, headlights. Convex: rear-view.
P = 1/f (metres), dioptre; powers add for lenses in contact.
Myopia–concave, hypermetropia–convex, presbyopia–bifocal, astigmatism–cylindrical, cataract–surgery.
TIR: diamond sparkle, optical fibre, mirage. Refraction: bent pencil, twinkling, early sunrise.
Prism: violet bends most. Sky blue, danger red, sunset red — scattering.
Practice: 22 questions
Sets of 10, mixed across the question types above. Every answer has a step-by-step explanation.
Topic test · 10 questions
Suggested time 3 min · wrong answers go to your mistake notebook automatically.