Optics

Concept Core

Mirrors, lenses, Snell's law, and Young's double slit — the complete optics framework.

Mirror Formula & Sign Convention

All distances measured from the pole of the mirror/centre of lens. Distances in direction of incident light are positive (+). Against incident light are negative (−).

Mirror formula: 1/v + 1/u = 1/f f = R/2 (f = focal length; R = radius of curvature) Magnification: m = −v/u

Concave mirror: f is negative (converging). Convex mirror: f is positive (diverging).

Refraction & Snell's Law

n₁ sinθ₁ = n₂ sinθ₂ (Snell's Law) n = c/v = speed of light in vacuum / speed in medium

Total internal reflection: when light goes from dense to rare medium at angle ≥ critical angle θ_c. sin θ_c = n₂/n₁ (where n₁ > n₂)

Lens Formula & Power

Lens formula: 1/v − 1/u = 1/f Lens maker's formula: 1/f = (n−1)(1/R₁ − 1/R₂) Power: P = 1/f (in metres) Unit: Dioptre (D) m = v/u (no minus sign for lens)

Lenses in contact: P = P₁ + P₂ or 1/f = 1/f₁ + 1/f₂

Young's Double Slit Experiment (YDSE)

Fringe width β = λD/d Bright fringes: path diff = nλ (n = 0,1,2...) Dark fringes: path diff = (2n−1)λ/2

d = slit separation, D = screen distance, λ = wavelength. Fringe width increases with larger D or λ, smaller d.

Single Slit Diffraction

Central maximum has double width of secondary maxima:

First dark fringe: a sinθ = λ → θ ≈ λ/a Central max width (angular): 2λ/a

Smaller slit (a) → broader diffraction pattern. Slit width a ≫ λ → geometric optics (negligible diffraction).

Optical Instruments — Human Eye

Near point: 25 cm (least distance of distinct vision, D)

Simple microscope (magnifying glass): m = 1 + D/f

Compound microscope: m = (L/f₀) × (D/fₑ) (L = tube length)

Telescope: m = f₀/fₑ (objective focal length / eyepiece focal length)

Formula Vault

All optics formulas — reflection, refraction, lenses, and wave optics.

Mirror Formula

1/v + 1/u = 1/f = 2/R

Sign convention: distances from pole

Mirror Magnification

m = −v/u

Negative = inverted image

Snell's Law

n₁ sinθ₁ = n₂ sinθ₂

n = c/v for each medium

Critical Angle

sin θ_c = n₂/n₁ = 1/n

Total internal reflection above θ_c

Lens Formula

1/v − 1/u = 1/f

Lens: no minus in magnification

Lens Power

P = 1/f (metres) in Dioptres

P₁+P₂ for lenses in contact

YDSE Fringe Width

β = λD/d

d=slit sep; D=screen dist

Bright Fringe Condition

Δ = nλ (n = 0,±1,±2,...)

Path difference = integer multiple of λ

Dark Fringe Condition

Δ = (2n−1)λ/2

Path difference = half-odd multiple of λ

Resolving Power (Telescope)

θ_min = 1.22λ/D

D = aperture diameter; Rayleigh criterion

Worked Examples

5 problems — mirror, lens, Snell's law, YDSE fringe width, and a classic sign-convention trap.

EasyObject 30 cm in front of concave mirror (f=20cm) — find image▾

An object is placed 30 cm in front of a concave mirror of focal length 20 cm. Find image position.

Sign convention: u = −30 cm (object in front), f = −20 cm (concave mirror)

Mirror formula: 1/v + 1/u = 1/f

1/v = 1/f − 1/u = 1/(−20) − 1/(−30) = −1/20 + 1/30 = −3/60 + 2/60 = −1/60

v = −60 cm (negative = real image in front of mirror)

✓ Image at 60 cm in front of mirror (real, inverted)

EasyFind critical angle for glass (n = 1.5) to air▾

Find the critical angle for total internal reflection when light goes from glass (n=1.5) to air.

sin θ_c = n_air/n_glass = 1/1.5 = 2/3

θ_c = sin⁻¹(2/3) ≈ 41.8°

✓ Critical angle = ≈ 41.8°

MediumYDSE: λ=600nm, d=0.1mm, D=1m — find fringe width▾

In YDSE, λ=600 nm, slit separation d=0.1 mm, screen distance D=1 m. Find fringe width.

β = λD/d = (600×10⁻⁹ × 1) / (0.1×10⁻³)

= 600×10⁻⁹ / 10⁻⁴ = 6×10⁻³ m = 6 mm

✓ Fringe width β = 6 mm

EAPCET LevelCombination of two lenses: f₁=20cm, f₂=−30cm — find effective focal length▾

Two thin lenses of focal lengths 20 cm and −30 cm are in contact. Find the effective focal length and power.

1/f = 1/f₁ + 1/f₂ = 1/20 + 1/(−30) = 3/60 − 2/60 = 1/60

f = 60 cm = 0.6 m

P = 1/f = 1/0.6 = +1.67 D

✓ f_eff = 60 cm, Power = +1.67 D (converging overall)

Trap QuestionMirror formula vs Lens formula sign differences — where students go wrong▾

An object 15 cm in front of a convex lens (f=10cm). A student uses 1/v+1/u = 1/f (mirror formula). What error occurs?

The trap: Mirror formula: 1/v + 1/u = 1/f. Lens formula: 1/v − 1/u = 1/f. The sign in the middle is different.

Using mirror formula for lens: 1/v = 1/f − 1/u = 1/10 − 1/(−15) = 1/10 + 1/15 = 5/30 = 1/6 → v = 6 cm ✗

Using correct lens formula: 1/v = 1/f + 1/u = 1/10 + 1/(−15) = 3/30 − 2/30 = 1/30 → v = 30 cm ✓

✓ Lens formula: 1/v − 1/u = 1/f; Mirror formula: 1/v + 1/u = 1/f — different sign!

Mistake DNA

4 optics errors from EAPCET distractor analysis.

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Using Mirror Formula for Lens (or Vice Versa)

Mirror: 1/v + 1/u = 1/f. Lens: 1/v − 1/u = 1/f. The central sign is different — confusing these is very common.

❌ Wrong

Lens problem: 1/v + 1/u = 1/f ✗ (that's mirror formula!)

✓ Correct

Lens: 1/v − 1/u = 1/f ✓ Mirror: 1/v + 1/u = 1/f ✓ Memory: Lens = L = minus

Memorise: LENS uses MINUS in the middle (1/v − 1/u). MIRROR uses PLUS (1/v + 1/u). This single distinction prevents the most common optics error.

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Sign Convention: Forgetting u is Negative for Object in Front

In Cartesian sign convention, the incident light travels left to right. Object in front of mirror/lens: u is negative.

❌ Wrong

Object 20cm in front: u = +20 cm ✗

✓ Correct

Incident light travels left to right. Object in front: u = −20 cm ✓ (against incident direction)

The sign convention: incident light direction is positive. Object is BEHIND the incoming light, so its distance is negative. Real object → u always negative.

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YDSE: Using d and D Incorrectly

In β = λD/d: D is the distance from slits to screen, d is the slit separation. Students swap these.

❌ Wrong

β = λd/D ✗ (d and D swapped; larger D should give bigger fringes)

✓ Correct

β = λD/d ✓ D = screen distance (large) d = slit separation (small) Bigger D → wider fringes

Intuition check: moving the screen farther (bigger D) spreads the fringes → β increases with D. Wider slit spacing (bigger d) compresses fringes → β decreases with d.

🌈

Total Internal Reflection: Wrong Direction

TIR occurs when light goes from denser to rarer medium (n₁ > n₂), NOT the reverse.

❌ Wrong

Light from air(n=1) to glass(n=1.5): TIR possible ✗ (going to denser medium)

✓ Correct

TIR: denser → rarer ✓ Glass(1.5) → air(1.0) ✓ At angle ≥ θ_c = sin⁻¹(n₂/n₁)

TIR requires the light to be going from a denser medium to a rarer one at a sufficiently large angle. The critical angle formula sin θ_c = n₂/n₁ only applies when n₁ > n₂.

Chapter Intelligence

Optics is split into ray optics and wave optics — both are tested in EAPCET.

EAPCET Weightage (2019–2024)

Mirrors and lenses (formula)

Refraction and Snell's law

YDSE (fringe width, conditions)

Total internal reflection

Optical instruments

Diffraction grating

High-Yield PYQ Patterns

Image position using mirror/lens formulaCritical angle calculationYDSE fringe width λD/dEffective focal length of combinationMagnification m = −v/u (mirror)Power of lens in dioptresSnell's law angle calculation

Exam Strategy

Sign convention: always write u as negative for real objects. f negative for concave mirror. Apply formulae with signs included.
Mirror formula: 1/v + 1/u = 1/f. Lens formula: 1/v − 1/u = 1/f. These are different — don't confuse them.
YDSE: β = λD/d is the fringe width. Bright = path diff nλ; Dark = (2n−1)λ/2. These appear as direct formula questions every year.
Power of lens: P = 1/f(metres) in Dioptres. Convex lens = positive P. Concave lens = negative P. Lenses in contact: P_total = P₁ + P₂.
Optics connects to Wave Physics (interference is a wave phenomenon) and Modern Physics (wave nature of light via photoelectric effect).

Concept Core

Formula Vault

Worked Examples

Mistake DNA

Chapter Intelligence

💡 Suggestions & Feedback

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