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Physics · NDA

Optics

📖 Chapter PN05 · NDA Class 11–12 Level 🎯 NDA Level : High Priority

Optics is the study of light and its behaviour — reflection, refraction, interference, and scattering. It is one of the highest-scoring chapters in NDA Physics, spanning ray optics (mirrors and lenses), optical instruments (eye, microscope, telescope, periscope), wave optics (interference and diffraction), and the scattering phenomena that explain everyday observations like the blue sky. Average students who learn the sign conventions and standard formulas can answer most NDA optics questions confidently.

📌 What to expect in NDA (based on 2022–2025 pattern):
(1) Mirror formula and magnification — concave and convex mirrors, image nature and position;
(2) Snell's law, refractive index, total internal reflection — critical angle;
(3) Lens formula, magnification, power of lens — converging and diverging;
(4) Human eye defects — myopia (short sight), hypermetropia (long sight) and their corrections;
(5) Optical instruments — microscope, telescope, periscope;
(6) Young's double-slit experiment — fringe width, constructive/destructive conditions;
(7) Scattering — Tyndall effect, blue sky, red sunset.

Topics at a Glance

① Reflection & Mirrors

Laws of reflection, mirror formula, concave/convex

② Refraction & Lenses

Snell's law, TIR, lens formula, power

③ Optical Instruments

Eye, microscope, telescope, periscope

④ Wave Optics & Scattering

YDSE, diffraction, Tyndall, blue sky

1. Reflection of Light & Mirrors

1.1

Laws of Reflection & Mirror Formula

The geometry of reflection — incident, normal, reflected ray

Reflection obeys two fundamental laws: (1) The incident ray, reflected ray, and normal at the point of incidence all lie in the same plane. (2) The angle of incidence equals the angle of reflection (∠i = ∠r). These hold for both plane and curved mirrors.

⚡ Mirror Formula & Magnification

Mirror Formula: 1/v + 1/u = 1/f = 2/R f = focal length (= R/2 for spherical mirror) R = radius of curvature u = object distance (from pole) v = image distance (from pole) Magnification: m = −v/u = h_image / h_object Sign Convention (New Cartesian — ALL distances from pole): Distances measured in direction of incident light → POSITIVE Distances measured opposite to incident light → NEGATIVE All real objects: u is NEGATIVE Concave mirror: f is NEGATIVE (focal point in front) Convex mirror: f is POSITIVE (focal point behind) Power of mirror: P = 1/f (in dioptres, f in metres) Note: power of mirror is NOT commonly used (unlike lenses)

Sign of magnification: m negative → image is inverted (real image). m positive → image is erect (virtual image). |m| > 1 → magnified; |m| < 1 → diminished.

Mirror Type	Object Position	Image Position	Nature	Application
Concave	At infinity	At F	Real, point	Solar cooker
Concave	Beyond C	Between F and C	Real, inverted, diminished	—
Concave	At C	At C	Real, inverted, same size	—
Concave	Between F & C	Beyond C	Real, inverted, magnified	Projectors
Concave	At F	At infinity	Real, parallel rays	Headlights, torches
Concave	Between P & F	Behind mirror	Virtual, erect, magnified	Shaving/dental mirror
Convex	Anywhere	Between P & F (behind)	Virtual, erect, diminished	Rear-view mirror, security

Fig. 1 — Concave mirror ray diagram (object beyond C). Ray 1 (blue): parallel to axis → reflects through F. Ray 2 (red): through C → reflects back. Image is real, inverted, diminished, between F and C.

💡 Mirror applications to remember: Concave mirrors — shaving/make-up (erect magnified), headlights (at F → parallel beam), solar cooker (at F → concentrated heat), doctor's head mirror. Convex mirrors — vehicle rear-view mirrors and security mirrors (always virtual, erect, wider field of view).

📝 TOPIC-WISE PYQ

Reflection & Mirrors — NDA Pattern Questions

Q1. An object is placed 30 cm in front of a concave mirror of focal length 15 cm. The image is formed at:

(a) 10 cm behind mirror (b) 30 cm in front (c) 30 cm behind (d) 15 cm in front

Answer: (b) 30 cm in front (real image at C)
1/v + 1/u = 1/f → 1/v + 1/(−30) = 1/(−15) → 1/v = −1/15 + 1/30 = −2/30 + 1/30 = −1/30. v = −30 cm. Negative → 30 cm in front (real image). Object at C → image at C.

Q2. Which mirror is used as a rear-view mirror in vehicles and why?

(a) Concave — magnifies objects (b) Convex — wider field of view (c) Plane — undistorted image (d) Concave — real image

Answer: (b) Convex — wider field of view
A convex mirror always forms a virtual, erect, and diminished image — covering a much wider field of view than a plane mirror of the same size. This lets the driver see more of the road behind. The image appears smaller but covers a large area.

Q3. A concave mirror of focal length 20 cm produces a virtual image at 10 cm. The object distance is:

(a) −6.67 cm (b) 6.67 cm (c) −10 cm (d) 20 cm

Answer: (a) −6.67 cm (object between P and F)
Virtual image behind mirror: v = +10 cm. 1/u = 1/f − 1/v = 1/(−20) − 1/10 = −1/20 − 2/20 = −3/20. u = −6.67 cm. Object is 6.67 cm in front of mirror — between pole and focus.

2. Refraction of Light & Lenses

2.1

Snell's Law, Refractive Index & Total Internal Reflection

Light bends at boundaries between media — and sometimes cannot escape at all

When light travels from one medium to another, it changes speed, causing refraction — a change in direction. The refractive index of a medium measures how much it slows light relative to vacuum. When light travels from denser to rarer medium at a large angle, it undergoes total internal reflection (TIR).

⚡ Refraction — Snell's Law & Refractive Index

Snell's Law: n₁ sin θ₁ = n₂ sin θ₂ (n = refractive index, θ = angle with normal) Refractive Index: n = c/v (speed of light in vacuum / speed in medium) n = sin i / sin r (for air→medium, i = incident angle in air) n_glass ≈ 1.5, n_water ≈ 1.33, n_air ≈ 1, n_diamond ≈ 2.42 Relative refractive index (medium 1 → medium 2): ₁n₂ = n₂/n₁ = sin θ₁ / sin θ₂ Total Internal Reflection (TIR): Condition: (1) Light goes from denser → rarer medium (2) Angle of incidence ≥ Critical angle (θ_c) Critical angle: sin θ_c = n_rarer / n_denser = 1/n (air side) For glass-air: sin θ_c = 1/1.5 → θ_c ≈ 42° For water-air: sin θ_c = 1/1.33 → θ_c ≈ 49° For diamond-air: sin θ_c = 1/2.42 → θ_c ≈ 24° (sparkling due to TIR!)

TIR applications: optical fibres (internet cables), endoscopes (medical cameras), diamond brilliance, mirage in deserts, periscope prisms. All require light in a denser medium hitting the boundary at ≥ critical angle.

Fig. 2 — Left: Refraction — light bends toward the normal entering a denser medium (θ₂ < θ₁). Right: Total Internal Reflection — light in denser medium strikes at θᵢ > θ_c; no refracted ray, all light reflects internally.

2.2

Lens Formula, Magnification & Power

Convex lenses converge light; concave lenses diverge — both described by the same formula

⚡ Lens Formula & Power

Lens Formula: 1/v − 1/u = 1/f Magnification: m = v/u = h_image / h_object Power of Lens: P = 1/f (unit: Dioptre, D; f in metres) Convex (converging) lens: f positive → P positive Concave (diverging) lens: f negative → P negative Lenses in contact: P_total = P₁ + P₂ + P₃ + ... 1/f_total = 1/f₁ + 1/f₂ + ... Lens Maker's Formula: 1/f = (n − 1)(1/R₁ − 1/R₂) n = refractive index of lens Sign convention (same as mirrors — all distances from optical centre): Real object: u negative Convex lens: f positive, concave lens: f negative

Power in dioptres: a +2D lens has f = 0.5 m (convex). A −3D lens has f = −0.33 m (concave). Higher dioptre = shorter focal length = stronger lens.

Lens	Nature of Image	Key Use	Power
Convex (converging)	Real & inverted (object beyond F); Virtual & erect (object inside F)	Camera, projector, magnifying glass, eye correction for hypermetropia	Positive (+)
Concave (diverging)	Always virtual, erect, diminished	Correction of myopia, peepholes in doors, wide-angle viewfinders	Negative (−)

📝 TOPIC-WISE PYQ

Refraction, TIR & Lenses — NDA Pattern Questions

Q1. The critical angle for glass-air interface is 42°. The refractive index of glass is approximately:

(a) 1.33 (b) 1.50 (c) 2.42 (d) 1.20

Answer: (b) 1.50
sin θ_c = 1/n → n = 1/sin 42° = 1/0.669 ≈ 1.49 ≈ 1.5. This is the standard refractive index of glass. (Diamond: n ≈ 2.42, θ_c ≈ 24°.)

Q2. An object is placed 20 cm from a convex lens of focal length 15 cm. The image is formed at:

(a) 60 cm (real) (b) 60 cm (virtual) (c) 12 cm (virtual) (d) 8.6 cm (real)

Answer: (a) 60 cm (real, inverted, magnified)
1/v − 1/u = 1/f → 1/v − 1/(−20) = 1/15 → 1/v = 1/15 − 1/20 = 4/60 − 3/60 = 1/60. v = +60 cm. Positive → real image on other side. Magnification = 60/20 = 3× (magnified).

Q3. Total internal reflection is used in optical fibres. The light travels through the fibre because:

(a) Refraction at every point (b) Repeated TIR at glass-air boundary (c) Diffraction (d) Interference

Answer: (b) Repeated TIR at glass-air boundary
Optical fibres are made of glass core surrounded by a cladding of lower refractive index. Light hitting the interface at ≥ critical angle undergoes TIR repeatedly and travels the full length of the fibre with minimal loss. Used in internet cables and medical endoscopes.

🤔 TRICKY QUESTIONS

Refraction & TIR — Conceptual Traps

T1. A fish underwater looks up at a fisherman standing at the bank. What does the fish see? What phenomenon explains this?

The fish sees the fisherman through a cone of half-angle 49° (the critical angle for water).
Light from above water entering water refracts toward the normal. The fish can only see the entire outside world compressed into a circular window (Snell's window) of angular radius 49°. Outside this cone, the surface acts like a mirror (TIR from water side). This is why fish appear much shallower than they are when viewed from above.

T2. A convex lens of focal length 10 cm and a concave lens of focal length 20 cm are placed in contact. What is the combined power and nature?

P = +5 D (converging), f = 20 cm.
P₁ = +1/0.10 = +10 D (convex). P₂ = −1/0.20 = −5 D (concave). P_total = 10 + (−5) = +5 D. Positive → combined lens is converging (convex nature). f = 1/P = 1/5 = 0.20 m = 20 cm. The convex lens dominates because it has shorter focal length (greater power).

3. Optical Instruments

3.1

Human Eye — Defects & Corrections

The eye as an optical instrument — and what goes wrong with it

The human eye works like a camera. The cornea and lens refract light to form a real, inverted image on the retina. The ciliary muscles adjust the lens curvature (accommodation) to focus on objects at different distances. The near point of a normal eye is 25 cm (least distance of distinct vision); the far point is at infinity.

👀 Myopia (Short-sightedness)

Far point is closer than infinity (e.g. at 2 m)
Eyeball too long OR lens too convex
Can see nearby objects clearly; cannot see distant objects
Image forms in front of the retina
Correction: Concave (diverging) lens
Power of lens = negative (−ve)

👀 Hypermetropia (Long-sightedness)

Near point is farther than 25 cm (e.g. at 1 m)
Eyeball too short OR lens too flat
Can see distant objects; cannot see nearby objects clearly
Image forms behind the retina
Correction: Convex (converging) lens
Power of lens = positive (+ve)

💡 Memory aid: Myopia → Myopic = near things only. Hypermetropia → Hyper = over-the-top distance. Correction: Myopia → concave (diverge to push image back); Hypermetropia → convex (converge to pull image forward). Presbyopia = old-age loss of accommodation (both near and far affected) → bifocal lenses.

⚡ Power of Corrective Lens Calculation

For Myopia: Far point = d (e.g. 2 m). Patient cannot see beyond d. Concave lens must form image of infinity AT the far point: v = −d, u = −∞ → 1/f = 1/v − 1/u = −1/d − 0 = −1/d Power P = −1/d (negative, in dioptres, d in metres) For Hypermetropia: Near point = D' (e.g. 1 m). Patient cannot see closer than D'. Convex lens must form image of 25 cm object AT near point: u = −0.25 m, v = −D' 1/f = 1/v − 1/u = 1/(−D') − 1/(−0.25) = −1/D' + 4 P = +1/f (positive, in dioptres)

3.2

Microscope, Telescope & Periscope

Instruments that extend human vision — principles and key formulas

Instrument	Principle	Key Formula	Defence Use
Simple Microscope (Magnifying glass)	Single convex lens; object inside F → virtual, erect, magnified	M = 1 + D/f (image at D = 25 cm) M = D/f (image at ∞)	Examining map details, evidence
Compound Microscope	Two convex lenses — objective (short f) forms real image; eyepiece magnifies that image	M = m_obj × m_eye = (L/f_o)(1 + D/f_e)	Forensic, medical labs
Astronomical Telescope	Objective (long f) forms real image at focal plane; eyepiece acts as magnifier	M = f_o/f_e (normal adjustment)	Artillery range estimation, navigation
Periscope	Two plane mirrors (or right-angle prisms) at 45° — using TIR or reflection	No magnification (M = 1); shifts line of sight by height h	Submarines, trench warfare observation

Fig. 3 — Periscope. Two plane mirrors (or right-angle prisms) at 45° redirect light through a height h. The line of sight shifts upward by h with no magnification. Used in submarines and military observation trenches.

📝 TOPIC-WISE PYQ

Eye Defects & Optical Instruments — NDA Pattern Questions

Q1. A person cannot see objects beyond 1.5 m. What type of lens and power is needed?

(a) Convex, +0.67 D (b) Concave, −0.67 D (c) Concave, −1.5 D (d) Convex, +1.5 D

Answer: (b) Concave, −0.67 D
Far point = 1.5 m → myopia. Needs concave lens. P = −1/d = −1/1.5 = −0.67 D. The concave lens diverges rays from infinity so they appear to come from the far point (1.5 m), which the eye can then focus.

Q2. The magnifying power of an astronomical telescope in normal adjustment with objective focal length 150 cm and eyepiece 5 cm is:

(a) 30 (b) 155 (c) 145 (d) 750

Answer: (a) 30
M = f_o/f_e = 150/5 = 30. For a telescope in normal adjustment, the final image is at infinity — formula is simply the ratio of focal lengths.

Q3. Periscopes are used in submarines. The optical element at 45° used in a modern periscope (for total internal reflection) is:

(a) Concave mirror (b) Convex lens (c) Right-angle prism (d) Plane mirror only

Answer: (c) Right-angle prism
Modern periscopes use right-angle (45°-45°-90°) glass prisms. Light undergoes TIR at each 45° face (since 45° > θ_c for glass ≈ 42°). Prisms give brighter images than mirrors (no silvering losses) and are more durable — important for military use.

🤔 TRICKY QUESTIONS

Eye & Instruments — Common Confusions

T1. For a telescope, what happens to magnification and resolving power when the diameter of the objective lens is increased?

Magnification unchanged; resolving power increases.
Magnification M = f_o/f_e — depends only on focal lengths, not on diameter. However, a larger objective aperture collects more light and reduces diffraction effects, improving resolving power (ability to distinguish two closely spaced objects). This is why large-aperture telescopes see finer detail despite similar magnification to smaller ones.

T2. An old person uses bifocal glasses. What defect do they have and what does each part of the bifocal lens correct?

Presbyopia — age-related loss of accommodation in both distances.
The upper part of a bifocal lens is a concave lens (corrects myopia — helps see distant objects). The lower part is a convex lens (corrects hypermetropia — helps read nearby text). Presbyopia occurs because ciliary muscles weaken with age, reducing the eye's ability to change lens curvature (accommodation). The lens itself also hardens, reducing flexibility.

4. Wave Optics & Scattering of Light

4.1

Young's Double-Slit Experiment (YDSE)

The definitive proof that light is a wave — alternating bright and dark fringes

Thomas Young's 1801 experiment proved the wave nature of light by demonstrating interference. When coherent light passes through two narrow slits, the overlapping waves create a pattern of alternating bright (constructive interference) and dark (destructive interference) fringes on a screen.

⚡ Young's Double-Slit Experiment Formulae

Setup: d = slit separation; D = distance from slits to screen; λ = wavelength Fringe width (β): β = λD/d (distance between adjacent bright/dark fringes) Constructive (bright fringe): path difference = nλ, n = 0, ±1, ±2, ... Destructive (dark fringe): path difference = (2n−1)λ/2 Position of nth bright fringe from centre: y_n = nλD/d Angular fringe width: θ = λ/d Effect of changes: β ∝ λ → longer wavelength → wider fringes β ∝ D → larger screen distance → wider fringes β ∝ 1/d → smaller slit separation → wider fringes In water (λ decreases): fringe width decreases

Central fringe is always bright (path difference = 0 → constructive). The experiment works only with coherent, monochromatic light. White light gives coloured fringes (different wavelengths give different fringe widths).

Fig. 4 — Young's Double-Slit Experiment. Coherent light from slits S₁ and S₂ interferes on the screen. Bright fringes (constructive): path difference = nλ. Dark fringes (destructive): path difference = (n+½)λ. Fringe width β = λD/d.

4.2

Diffraction & Scattering of Light

Why light bends around edges — and why the sky is blue

🔄 Single-Slit Diffraction

Light bends around edges of narrow opening (width a)
Central maximum is widest and brightest
First minimum: sinθ = λ/a
Width of central maximum = 2λD/a
Narrower slit → wider diffraction pattern (inverse)
Used to measure wavelength of light

🔴 Scattering — Tyndall Effect

Scattering ∝ 1/λ⁴ (shorter λ → scattered more)
Blue light (λ short) scattered most; Red light least
Tyndall effect: scattering of light by colloid particles
Blue sky: blue scattered in all directions from atmosphere
Red sunset: long path → blue removed, red transmitted
Milk appears white: scatters all wavelengths equally (larger particles)

⚡ Scattering & Key Wavelength Facts

Rayleigh Scattering: I_scattered ∝ 1/λ⁴ (intensity scattered) Visible spectrum (approximate wavelengths): Violet: 380–420 nm (scattered MOST — shortest λ) Blue: 420–490 nm (scattered a lot — blue sky) Green: 490–560 nm Yellow: 560–590 nm Orange: 590–625 nm Red: 625–750 nm (scattered LEAST — red sunset/danger signals) VIBGYOR: Violet Indigo Blue Green Yellow Orange Red (increasing wavelength →; decreasing frequency →) Speed of light in vacuum: c = 3 × 10⁸ m/s All colours travel at same speed in vacuum (different in media)

Red is used for danger signals, stop lights, and taillights because it scatters least through fog and dust — it travels farthest with least loss of intensity.

⚠ NDA Exam Trap — Why is the sky blue and sunset red?
Blue sky: Sunlight enters atmosphere; blue light (λ short) is scattered by gas molecules in all directions (Rayleigh scattering, I ∝ 1/λ⁴). An observer looking anywhere in the sky receives scattered blue light → sky appears blue.
Red sunset: At sunrise/sunset, light travels through a much longer atmospheric path. Almost all blue, violet, and green light is scattered away before reaching the observer. Only longer-wavelength red and orange light survives to reach the eye → red/orange sunset.

📝 TOPIC-WISE PYQ

Wave Optics & Scattering — NDA Pattern Questions

Q1. In Young's double-slit experiment, fringe width is β. If the slit separation is doubled keeping everything else constant, the new fringe width is:

(a) 2β (b) β/2 (c) β/4 (d) 4β

Answer: (b) β/2
β = λD/d. Doubling d: β' = λD/(2d) = β/2. Fringe width is inversely proportional to slit separation. Wider slit separation → fringes closer together (narrower).

Q2. The sky appears blue because of:

(a) Reflection from sea (b) Scattering of blue light by atmosphere (c) Blue colour of space (d) Absorption by atmosphere

Answer: (b) Scattering of blue light by atmosphere
Rayleigh scattering: I ∝ 1/λ⁴. Blue light (short wavelength) is scattered far more than red. Scattered blue light reaches the observer from all directions — making the entire sky appear blue. This is the Tyndall effect applied to the atmosphere.

Q3. In YDSE, if the experiment is immersed in water (n = 1.33), the fringe width:

(a) Increases (b) Decreases (c) Remains same (d) Becomes zero

Answer: (b) Decreases
In water, wavelength λ' = λ/n = λ/1.33. Since β = λD/d, and λ decreases in water, β' = λ'D/d = β/1.33. Fringe width decreases by a factor of 1.33.

🤔 TRICKY QUESTIONS

Wave Optics & Scattering — Reasoning Traps

T1. In YDSE, one of the slits is covered. What happens to the interference pattern?

Interference pattern disappears — only a single-slit diffraction pattern remains.
Interference requires two coherent sources. With one slit covered, there is no second wave to interfere with. The screen shows a broad, single-slit diffraction pattern (central bright band with decreasing side bands) instead of the regular bright and dark fringes of YDSE. Also, the total intensity on screen is halved (one source removed).

T2. Danger signals and rear lights of vehicles are red. Traffic lights in fog use red. Why not use violet (even shorter wavelength — more visible)?

Red scatters least in fog, dust, and atmosphere — travels farthest.
Although violet and blue are more intensely scattered (seen more in clear air), in foggy or dusty conditions this same scattering causes rapid intensity loss — the signal cannot be seen from far away. Red light (λ largest in visible) scatters least (I ∝ 1/λ⁴), maintaining its intensity over long distances through fog and dust. It reaches the observer with the least attenuation — making it ideal for emergency and warning signals.

⚡ High-Yield Formula Sheet — PN05 Optics

🔴 Mirrors

1/v + 1/u = 1/f = 2/R
m = −v/u (negative → inverted)
Concave: f negative; Convex: f positive
All distances from pole; real object: u −ve

🔎 Refraction & TIR

n₁ sinθ₁ = n₂ sinθ₂ (Snell's law)
n = c/v = sin i/sin r
sin θ_c = n_rarer/n_denser = 1/n
Glass: θ_c ≈ 42°; Water: ≈ 49°; Diamond: ≈ 24°

🔴 Lenses

1/v − 1/u = 1/f
m = v/u; P = 1/f (D)
P_total = P₁ + P₂ (in contact)
Convex: f +ve, P +ve; Concave: f −ve, P −ve

👀 Eye Defects

Myopia: far point < ∞ → concave lens (−ve P)
P_myopia = −1/far point (m)
Hypermetropia: near point > 25 cm → convex (+ve P)
Presbyopia: old-age → bifocal lenses

🔬 Instruments

Simple microscope: M = 1 + D/f (D=25 cm)
Telescope (normal): M = f_o/f_e
Periscope: M = 1 (no magnification)
Compound microscope: M = m_obj × m_eye

🌈 Wave Optics & Scattering

YDSE: β = λD/d
Bright: path diff = nλ; Dark: (n+½)λ
Scattering: I ∝ 1/λ⁴ (Rayleigh)
Blue sky: blue scattered most
Red sunset: red travels farthest

📌 Key numbers: D (near point) = 25 cm; n_glass ≈ 1.5; n_water ≈ 1.33; n_diamond ≈ 2.42; θ_c (glass-air) ≈ 42°; c = 3×10⁸ m/s; VIBGYOR: V(380 nm) → R(750 nm).

⚡ Quick Revision Booster — PN05 Optics

🔴 Mirror Rules

Concave f: −ve; Convex f: +ve (new Cartesian)
Real object → u always negative
m −ve → inverted (real); m +ve → erect (virtual)
Concave at F → parallel beam (headlights, torch)
Convex → always virtual, erect, diminished (rear-view)

🔎 TIR Facts

Denser → rarer + angle ≥ θ_c → TIR
Glass θ_c ≈ 42°; Diamond ≈ 24° (sparkle!)
Optical fibre: repeated TIR (internet cables)
Mirages, looming: TIR in atmosphere (hot/cold air)
Endoscope: TIR in flexible glass fibres

👀 Eye Defects

Myopia: far point short → concave lens (−ve P)
Hypermetropia: near point too far → convex (+ve P)
Presbyopia: old age → bifocal lenses
Near point normal eye = 25 cm
Power correction = 1/focal length (metres)

🔬 Instruments

Telescope: M = f_o/f_e (large f_o, small f_e)
Simple microscope: object inside F of convex lens
Periscope: two 45° mirrors or right-angle prisms (TIR)
Larger telescope objective → better resolving power
Doctor's head mirror = concave (magnified real image)

🌈 YDSE

β = λD/d → β ∝ λ, β ∝ D, β ∝ 1/d
Central fringe = always bright (path diff = 0)
In water: λ decreases → β decreases
Wider slits → narrower fringes
Coherent, monochromatic light required

🚨 Scattering Traps

Scattering: I ∝ 1/λ⁴ — blue most, red least
Blue sky: blue scattered in all directions
Red sunset: blue filtered out over long path
Red for danger: least scattered in fog/dust
Milk white: all wavelengths scattered equally (fat globules)

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