Olive Defence

Physics · CDS

PC07 — Optics: Light & Its Applications

📖 PC07 · CDS General Science — Physics 🎯 CDS Level : High Priority

Optics is one of the most visual and intuitive chapters in CDS Physics. It explains mirrors, lenses, the human eye, and why the sky is blue. Mirror and lens formulae, the sign convention, and real-world applications such as corrective glasses and microscopes are directly and repeatedly tested.

📌 CDS focuses on:
(1) Reflection — laws, plane mirror image properties, concave vs convex mirrors;
(2) Refraction — Snell's law, refractive index, total internal reflection;
(3) Lenses — types, focal length, lens formula, power of lens;
(4) Human eye — parts, near/far sightedness, corrections with lenses;
(5) Optical instruments — microscope, telescope, periscope;
(6) Dispersion — rainbow formation, why sky is blue (Tyndall effect).

Topics at a Glance

① Reflection of Light

Laws, plane & spherical mirrors, image types

② Refraction

Snell's law, refractive index, TIR

③ Lenses

Convex, concave; lens formula; power

④ Human Eye

Parts, defects, corrections

⑤ Optical Instruments

Microscope, telescope, periscope

⑥ Dispersion & Scattering

Rainbow, blue sky, Tyndall effect

1. Reflection of Light

1.1

Laws of Reflection & Mirror Types

Light bouncing off surfaces — predictable and calculable

Two Laws of Reflection:
1. The angle of incidence (∠i) = angle of reflection (∠r), both measured from the normal.
2. The incident ray, normal, and reflected ray all lie in the same plane.

Fig. 1 — The angle of incidence always equals the angle of reflection. Both angles are measured from the dashed normal (perpendicular to the mirror surface), not from the mirror itself.

📍 Concave Mirror (Converging)

Reflects from inner curved surface (cave-like)
Converges parallel rays to a focus
Can form real (inverted) or virtual (erect, magnified) images depending on object position
Uses: torchlight reflectors, dental mirrors, solar cookers, headlights
For object beyond C: real, inverted, diminished image

📍 Convex Mirror (Diverging)

Reflects from outer curved surface (bulging outward)
Diverges parallel rays — rays appear to come from behind mirror
Always forms virtual, erect, and diminished image
Uses: rear-view mirrors in vehicles (wider field of view)
Cannot form real images

⚡ Mirror Formula & Magnification

Mirror formula: 1/f = 1/v + 1/u f = focal length; v = image distance; u = object distance Magnification: m = −v/u = h_image / h_object Sign Convention (New Cartesian): Object always placed to the LEFT of the mirror. All distances measured from the pole (centre) of mirror. Distances in direction of incident light → positive (+) Distances opposite to incident light → negative (−) For concave mirror: f is NEGATIVE (focal point in front of mirror) For convex mirror: f is POSITIVE (focal point behind mirror)

2. Refraction of Light

2.1

Snell's Law & Refractive Index

Light bends when it crosses from one medium to another

Refraction occurs because light changes speed when it enters a different medium. It bends toward the normal when entering a denser medium, and away from the normal when entering a less dense medium.

Fig. 2 — Refraction at the air-glass boundary. Light bends toward the normal when entering a denser medium. The ratio of sines of the angles obeys Snell's Law: n₁ sin i = n₂ sin r.

⚡ Refraction Formulae & Key Values

Snell's Law: n₁ sin(∠i) = n₂ sin(∠r) Refractive index: n = speed of light in vacuum / speed in medium n = c / v (c = 3 × 10⁸ m/s) n of vacuum/air = 1.0 n of water = 1.33 n of glass = 1.5 n of diamond = 2.42 Total Internal Reflection (TIR): Occurs when light goes from DENSER to RARER medium AND the angle of incidence exceeds the critical angle. Critical angle C: sin C = n₂/n₁ (n₂ < n₁) Critical angle for glass-air: C ≈ 42° For diamond-air: C ≈ 24° (very small → TIR easy → diamond sparkles)

TIR applications: optical fibres (internet cables, endoscopes), mirage in desert, apparent depth of swimming pool, diamond brilliance.

⚠ CDS Refraction Trap: A stick placed in water appears bent (broken) at the surface. The stick hasn't changed — it's refraction of light at the water-air interface that makes it look bent. Also: objects in water appear closer (shallower) than they are — apparent depth = real depth / n.

📝 CDS PYQ

Reflection & Refraction

Q1. Which type of mirror is used as a rear-view mirror in vehicles?

(a) Concave (b) Convex (c) Plane (d) Both concave and convex

Answer: (b) Convex mirror
Convex mirrors always form virtual, erect, and diminished images. This gives a wider field of view — a driver can see more of the road behind. Even though objects appear smaller, the advantage of seeing a wide area outweighs the size reduction. Concave mirrors cannot be used as rear-view mirrors as they form inverted real images for distant objects.

Q2. A ray of light passes from air into glass. Which of the following is correct?

(a) It bends away from the normal (b) It bends toward the normal (c) It continues in the same direction (d) It is totally reflected

Answer: (b) It bends toward the normal
When light enters a denser medium (glass is denser than air, n_glass = 1.5 > n_air = 1.0), it slows down and bends toward the normal. This means the angle of refraction is smaller than the angle of incidence. Total Internal Reflection occurs only when going from denser to rarer (glass → air), not air → glass.

Q3. Optical fibres work on the principle of:

(a) Refraction (b) Reflection (c) Total internal reflection (d) Dispersion

Answer: (c) Total internal reflection
In optical fibres, light travels through a dense glass core surrounded by a less dense cladding. Light hits the boundary at an angle greater than the critical angle, causing total internal reflection — 100% of light is reflected back inside. This allows signals to travel thousands of kilometres with minimal loss. Used in: internet cables, medical endoscopes, decorative lamps.

3. Lenses

3.1

Convex & Concave Lenses

Refraction through curved glass — the basis of all optical instruments

Fig. 3 — A convex (converging) lens brings parallel rays to a single point called the principal focus (F). The distance from the lens centre to F is the focal length.

⚡ Lens Formula & Power

Lens formula: 1/f = 1/v − 1/u Magnification: m = v/u = h_image / h_object Power of lens: P = 1/f (f in metres) Unit of power: Dioptre (D) Sign Convention for lenses (New Cartesian): Object on the left, all distances from optical centre. Distances to the right → positive (+) Distances to the left → negative (−) Convex lens: f is POSITIVE; Concave lens: f is NEGATIVE Combined lenses: P_total = P₁ + P₂ + P₃ + ... (in dioptres)

A spectacle lens of power +2 D is a convex lens with f = 1/2 = 0.5 m = 50 cm. A −3 D lens is concave with f = −0.33 m. The eye doctor's prescription gives power in dioptres.

4. The Human Eye & Its Defects

4.1

Eye Structure & Corrective Lenses

The eye is a natural convex lens system — and its defects are fixed with spectacles

Fig. 4 — Human eye structure (left) and the three main vision defects with their corrections. Myopia is corrected by concave (diverging) lenses; hypermetropia by convex (converging) lenses.

5. Dispersion, Rainbow & Scattering

5.1

Why Rainbows Form & Why the Sky is Blue

Dispersion splits white light into colours; scattering explains the colour of sky

🌌 Dispersion of White Light

White light splits into 7 colours when passing through a prism: VIBGYOR (Violet, Indigo, Blue, Green, Yellow, Orange, Red)
Violet is deviated most; Red is deviated least
Different colours have different refractive indices in glass
Rainbow: Sunlight undergoes dispersion + total internal reflection inside water droplets. Produced when Sun is behind you and rain in front
Red arc is outermost; Violet is innermost

🔆 Scattering — Why Sky is Blue

Tyndall Effect: Scattering of light by particles in a medium
Shorter wavelengths (blue, violet) are scattered more than longer wavelengths (red)
Blue has ~10× more scattering than red by air molecules
Sky appears blue because blue light scatters in all directions and reaches our eyes
Sunrise/Sunset red: Sun is near horizon → light travels long path through atmosphere → blue is completely scattered away → red remains

⚠ Dispersion CDS Traps: (1) In a spectrum, violet has the shortest wavelength and highest frequency — it deviates the most in a prism. Red has the longest wavelength — it deviates the least. (2) The sequence VIBGYOR goes from most-deviated (violet) to least-deviated (red). (3) Sky is blue due to scattering — NOT reflection or dispersion.

📝 CDS PYQ

Optics — Lenses, Eye & Light

Q1. A person cannot see objects clearly beyond 50 cm. What type of defect does he have and what lens corrects it?

(a) Hypermetropia; convex lens (b) Myopia; concave lens (c) Myopia; convex lens (d) Presbyopia; bifocal lens

Answer: (b) Myopia; corrected by a concave lens
Inability to see distant objects = myopia (near-sightedness). The eye's lens system is too strong, forming images in front of the retina. A concave (diverging) lens spreads the rays before they enter the eye, effectively shifting the image back to the retina. The person's far point is 50 cm, so he needs a concave lens of focal length 50 cm (Power = −2 D).

Q2. The sky appears blue because of:

(a) Reflection of sunlight by the sea (b) Dispersion of sunlight by water vapour (c) Preferential scattering of blue light by air molecules (d) Absorption of all other colours by the atmosphere

Answer: (c) Preferential scattering of blue light by air molecules
When sunlight passes through the atmosphere, shorter wavelengths (blue/violet) are scattered much more than longer wavelengths (red/orange) — this is Rayleigh scattering (related to the Tyndall effect). Scattered blue light reaches our eyes from all directions, making the sky appear blue. At sunrise/sunset, light travels a longer path, so blue is completely scattered away and only red/orange reach us.

Q3. A convex lens has a focal length of 25 cm. Its power is:

(a) 4 D (b) −4 D (c) 25 D (d) 0.25 D

Answer: (a) +4 D
Power of a lens P = 1/f (f in metres). f = 25 cm = 0.25 m. P = 1/0.25 = +4 D. Convex lenses have positive focal length and positive power; concave lenses have negative power. Dioptres are used in spectacle prescriptions — a "+4 D" prescription means convex lens of power 4 dioptres.

📚 Formula Sheet — PC07 Optics

📻 Mirrors

1/f = 1/v + 1/u (mirror formula)
m = −v/u (magnification)
Concave: f negative (real focus)
Convex: f positive (virtual focus)
Concave = converging; Convex = diverging

🔭 Refraction

n₁ sin i = n₂ sin r (Snell's Law)
n = c / v (refractive index)
n_glass = 1.5; n_water = 1.33
Apparent depth = Real depth / n
TIR: denser → rarer; angle > critical angle

🔭 Lenses

1/f = 1/v − 1/u (lens formula)
P = 1/f (D); P_total = P₁ + P₂
Convex: f +ve, converging
Concave: f −ve, diverging
Normal near point of eye = 25 cm

🎊 Eye Defects

Myopia (short-sight): concave lens
Hypermetropia (long-sight): convex lens
Presbyopia (age): bifocal
VIBGYOR: Violet=most deviated, Red=least
Blue sky: Rayleigh/Tyndall scattering

⚡ Quick Revision Booster — PC07

📻 Mirror Types

Concave: converging; real focus
Convex: diverging; virtual, erect, diminished
Rear-view: convex (wide field)
Dental/torch: concave
1/f = 1/v + 1/u

🔭 Refraction

Dense → rarer: bends away from normal
Rarer → dense: bends toward normal
TIR: dense to rarer + angle > critical
Diamond sparkles: very small critical angle (~24°)
Optical fibre: TIR keeps signal inside

🔭 Lens Power

P = 1/f (metres), unit: Dioptre
Convex: +ve power
Concave: −ve power
Combined: P_total = P₁ + P₂
f = 50 cm → P = +2 D

🔆 Eye Facts

Myopia: far-sighted? No — NEAR sighted
Hypermetropia: FAR sighted
Near point: 25 cm; Far point: infinity
Myopia: concave correction
Hypermetropia: convex correction

🌌 Spectrum & Colours

VIBGYOR — Violet to Red
Violet: shortest wavelength, most bent
Red: longest wavelength, least bent
Rainbow: Red outside, Violet inside
Sunset red: blue scattered away, red remains

🚨 CDS Traps

Myopia → concave (NOT convex)
Hypermetropia → convex (NOT concave)
Sky blue → scattering (NOT dispersion)
Sunset red → blue scattered away
Apparent depth < actual depth (water)

📝 Practice Exercise

Attempt these on your own first.

E-01

A concave mirror has focal length 20 cm. An object is placed 60 cm from the mirror. The image distance is:

(a) 30 cm
(b) −30 cm
(c) 20 cm
(d) −60 cm

E-02

A ray of light passes from glass (n=1.5) to air. Total internal reflection will occur when the angle of incidence is:

(a) Greater than the critical angle
(b) Less than the critical angle
(c) Equal to the angle of refraction
(d) Zero degrees

E-03

A person uses a −2.5 D lens. What type of defect does she have?

(a) Hypermetropia
(b) Presbyopia
(c) Myopia
(d) Astigmatism

E-04

A diamond sparkles more than glass due to:

(a) Refraction
(b) Dispersion
(c) Total internal reflection (very small critical angle)
(d) High transparency

E-05

In a rainbow, which colour is on the outer (top) arc?

(a) Violet
(b) Blue
(c) Green
(d) Red

Answers: E-01: (a) 30 cm [1/f=1/v+1/u; f=−20cm (concave,−ve), u=−60cm; 1/v = 1/f − 1/u = −1/20 + 1/60 = −3/60+1/60 = −2/60; v = −30 cm; 30 cm in front of mirror] | E-02: (a) Greater than the critical angle — TIR occurs only above the critical angle | E-03: (c) Myopia — negative lens power means concave lens, which corrects myopia | E-04: (c) Total internal reflection — diamond's critical angle is only ~24°, so most light undergoes TIR inside and sparkles brilliantly | E-05: (d) Red — Red is least deviated and forms the outermost arc; Violet is innermost

📝 Mock Tests 🎯 Subject Quizzes ✈️ Telegram