Optics – JEE Main Physics Formula Sheet & Class 12 Notes | Mirror Formula, Snell's Law, Lens Formula, TIR, Prism, Young's Double Slit, Diffraction, Polarisation & All Optics Formulas

Reflection of Light — Mirror Formula, Magnification, Mirror Types

Why Mirror Formula 1/v+1/u=1/f and Magnification m=–v/u Are the Most-Tested Ray Optics JEE Main Results

Laws of Reflection (from Aakash PDF — Optics JEE Main):

(1) The angle of incidence (i) equals the angle of reflection (r): i = r.

(2) The incident ray, normal, and reflected ray are all in the same plane.

These laws hold for all reflecting surfaces (plane mirror, concave mirror, convex mirror).

Sign Convention (from Aakash PDF — Optics JEE Main):

All distances measured from the pole of the mirror. Distances in the direction of incident light (before mirror) = positive. Distances opposite to incident light (behind mirror) = negative for real objects/images in front, positive behind.

For standard setup (object to left, light moving right): object distance u is negative (u<0 for real object). f<0 for concave mirror (converging). f>0 for convex mirror (diverging).

Mirror Formula (from Aakash PDF — Optics JEE Main):

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

f = focal length; R = radius of curvature; f = R/2 for all spherical mirrors.

Linear magnification: m = –v/u

m > 0: erect (virtual) image. m < 0: inverted (real) image. |m| > 1: magnified. |m| < 1: diminished.

Other forms: m = f/(f–u) = (f–v)/f.

Concave Mirror (from Aakash PDF — Optics JEE Main):

f < 0 (focal point in front of mirror). Key positions:

Object at infinity: image at F (real, inverted, diminished). Object beyond C: image between F and C (real, inverted, diminished). Object at C: image at C (real, inverted, same size). Object between F and C: image beyond C (real, inverted, magnified). Object at F: image at infinity. Object between F and P: image behind mirror (virtual, erect, magnified).

Convex Mirror (from Aakash PDF — Optics JEE Main):

f > 0. Image always virtual, erect, diminished (regardless of object position). Used as rear-view mirror (wide field of view). Image always between F and P behind the mirror.

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Refraction — Snell's Law, Refractive Index, TIR, Glass Slab, Spherical Surface

Why Snell's Law n₁sinθ₁=n₂sinθ₂ and Critical Angle sinC=1/n Are the Most-Tested Refraction JEE Main Formulas

Snell's Law and Refractive Index (from Aakash PDF — Optics JEE Main):

n₁ sinθ₁ = n₂ sinθ₂ (Snell's law at interface between media with n₁ and n₂)

Absolute refractive index: n = c/v (speed of light in vacuum / speed in medium)

n > 1 always (light slows down in any medium). Air: n ≈ 1. Water: n ≈ 4/3. Glass: n ≈ 1.5.

Relative refractive index: ₁n₂ = n₂/n₁ = v₁/v₂ (ratio of speeds)

Real and Apparent Depth (from Aakash PDF — Optics JEE Main):

Object in denser medium (n), viewed from rarer medium (air, n=1):

Apparent depth = Real depth / n

Apparent shift (upward) = Real depth – Apparent depth = Real depth × (1 – 1/n)

n = Real depth / Apparent depth

When viewed from denser medium (n) into rarer: apparent depth = n × Real depth (appears deeper).

Lateral Shift in Glass Slab (from Aakash PDF — Optics JEE Main):

Ray passing through a glass slab (thickness t, refractive index n, angle of incidence i, angle of refraction r):

Lateral shift d = t × sin(i–r)/cosθᵣ = t × sinδ/cosθᵣ

The ray exits parallel to the incident ray but laterally displaced. No angular deviation.

Total Internal Reflection (TIR) (from Aakash PDF — Optics JEE Main):

When light travels from denser (n₁) to rarer (n₂) medium and angle of incidence exceeds critical angle C:

Critical angle: sinC = n₂/n₁

If n₂ = 1 (air): sinC = 1/n₁ → C = sin⁻¹(1/n)

Higher n → smaller C (more likely to have TIR). For glass (n=1.5): C = sin⁻¹(1/1.5) = sin⁻¹(0.667) ≈ 42°.

Conditions for TIR: (1) Light must travel from denser to rarer. (2) Angle of incidence > C.

Applications: optical fibre (total internal reflection keeps light inside the core), diamond sparkling (high n→small C→multiple TIR), mirage, prism reflectors (45° prism → θ>42°→TIR).

Refraction at Spherical Surface (from Aakash PDF — Optics JEE Main):

At a single spherical refracting surface separating media n₁ and n₂, centre of curvature at C, radius R:

n₂/v – n₁/u = (n₂–n₁)/R

Sign convention: same as mirrors — all distances from pole, incident light direction positive.

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Prism — Deviation, Minimum Deviation, Refractive Index, Dispersion

Why Prism Formula n=sin((A+Dm)/2)/sin(A/2) and Thin Prism δ=(n–1)A Are the Most-Tested Prism JEE Main Formulas

Prism Terminology (from Aakash PDF — Optics JEE Main):

A prism has apex angle A (angle at the top), two refracting faces. Angle of incidence at first face = i, angle of refraction inside = r₁. Angle of incidence inside at second face = r₂, angle of emergence = e.

Geometry: r₁ + r₂ = A

Total deviation: δ = i + e – A

Minimum Deviation (from Aakash PDF — Optics JEE Main):

Deviation δ is minimum when the ray passes symmetrically through the prism:

i = e (angle of incidence = angle of emergence)

r₁ = r₂ = A/2 (ray inside is parallel to base)

At minimum deviation Dm:

n = sin((A+Dm)/2) / sin(A/2)

This is the standard formula for finding refractive index of prism material using minimum deviation experiment.

Deviation by Thin Prism (from Aakash PDF — Optics JEE Main):

For a prism with very small apex angle A (thin prism, A in radians):

δ = (n–1)A (angle of deviation)

Valid for small A and near-normal incidence.

Dispersion (from Aakash PDF — Optics JEE Main):

Different wavelengths of light have different refractive indices (n_v > n_r for violet > red). A prism separates white light into its constituent colours (VIBGYOR from bottom to top for upward deviation).

Angular dispersion: Δδ = (n_v – n_r)A

Dispersive power: ω = (n_v – n_r)/(n_y – 1)

where n_y = refractive index for yellow (mean) light.

Mean deviation: δ_y = (n_y – 1)A.

Deviation without dispersion (achromatic combination): two prisms with ω₁A₁ = ω₂A₂ (but different materials) → net dispersion=0, net deviation≠0.

Dispersion without deviation: δ₁ = –δ₂ → (n_y1–1)A₁ = (n_y2–1)A₂ (but angular dispersions don't cancel).

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Thin Lens — Lens Maker's Equation, Lens Formula, Power, Lens Combinations

Why Lens Formula 1/v–1/u=1/f, Power P=1/f, and Lenses in Contact P=P₁+P₂ Are the Most-Tested Optics JEE Main Formulas

Lens Maker's Equation (from Aakash PDF — Optics JEE Main):

For a thin lens of refractive index n (in air), radii of curvature R₁ (first surface) and R₂ (second surface):

1/f = (n–1)(1/R₁ – 1/R₂)

Sign convention: R₁ positive if centre of curvature is to the right; R₂ positive if centre is to the right.

Biconvex lens: R₁ > 0, R₂ < 0 → 1/f = (n–1)(1/R₁+1/|R₂|) > 0 → converging.

Biconcave lens: R₁ < 0, R₂ > 0 → 1/f < 0 → diverging.

If immersed in medium of index n_m: replace (n–1) with (n/n_m–1).

Thin Lens Formula (from Aakash PDF — Optics JEE Main):

1/v – 1/u = 1/f

Magnification: m = v/u = (v–f)/f = f/(f+u)

m > 0: erect image (virtual). m < 0: inverted image (real). |m| > 1: magnified. |m| < 1: diminished.

Newton's lens formula: x₁x₂ = f² where x₁ = object distance from focus, x₂ = image distance from focus.

Convex Lens Image Formation (from Aakash PDF — Optics JEE Main):

Object at infinity: image at F₂ (real, inverted, point). Object beyond 2F: image between F and 2F (real, inverted, diminished). Object at 2F: image at 2F (real, inverted, same size). Object between F and 2F: image beyond 2F (real, inverted, magnified). Object at F: image at infinity. Object between F and O: image on same side as object (virtual, erect, magnified — acts as magnifying glass).

Power of a Lens (from Aakash PDF — Optics JEE Main):

P = 1/f (metres) or P = 100/f (centimetres). Unit: Dioptre (D). Convex (converging): P > 0. Concave (diverging): P < 0.

Lenses in Contact (from Aakash PDF — Optics JEE Main):

1/F = 1/f₁ + 1/f₂ + ... = Σ(1/fᵢ)

P_total = P₁ + P₂ + ...

Lenses Separated by Distance d (from Aakash PDF — Optics JEE Main):

1/F = 1/f₁ + 1/f₂ – d/(f₁f₂)

For zero power (P=0): d = f₁+f₂ (Galilean telescope condition).

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Optical Instruments — Simple Microscope, Compound Microscope, Telescope

Why Microscope and Telescope Magnification Formulas Are Direct Optics JEE Main Questions

Simple Microscope (Magnifying Glass) (from Aakash PDF — Optics JEE Main):

A single convex lens held close to the eye. D = least distance of distinct vision = 25 cm.

Image at infinity (relaxed eye): m = D/f

Image at near point (near-point accommodation): m = 1 + D/f

Shorter focal length → higher magnification. For f=5cm: m=5 (at infinity) or m=6 (near point).

Compound Microscope (from Aakash PDF — Optics JEE Main):

Objective (short f_o): forms real, inverted, magnified image at distance L (tube length) beyond its focus. Eyepiece (short f_e): acts as simple microscope viewing this image.

Magnification of objective: m_o = –L/f_o (approximately, for final image at infinity)

Magnification of eyepiece: m_e = D/f_e (image at infinity)

Total magnification: m = m_o × m_e = –(L/f_o)(D/f_e)

Negative sign indicates inverted image. L = tube length (distance from back focal point of objective to front focal point of eyepiece). Actual total length ≈ L + f_o + f_e.

Astronomical Telescope (from Aakash PDF — Optics JEE Main):

Objective (long f_o, large aperture): forms real image of distant object at its focal plane. Eyepiece (short f_e): views this image.

Normal adjustment (final image at infinity, relaxed eye): image formed at F_o coincides with F_e.

Angular magnification: m = –f_o/f_e (negative = inverted)

Length of telescope: L = f_o + f_e

Near-point adjustment: m = –(f_o/f_e)(1 + f_e/D)

Galilean Telescope (from Aakash PDF — Optics JEE Main):

Objective: convex (f_o). Eyepiece: concave (–f_e).

m = f_o/f_e; Length = f_o – f_e (shorter than astronomical). Erect image. Less magnification than astronomical.

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Wave Optics — Young's Double Slit, Interference Intensity, Fringe Pattern

Why Fringe Width β=λD/d, Path Difference Δ=yd/D, and Intensity I=4I₀cos²(δ/2) Are the Most-Tested Wave Optics JEE Main Formulas

Huygens' Principle and Coherence (from Aakash PDF — Optics JEE Main):

Huygens' principle: Every point on a wavefront is the source of secondary spherical wavelets. The new wavefront is the envelope of these secondary wavelets.

Coherent sources: sources with constant phase difference (same frequency, fixed phase relationship). Required for sustained interference pattern.

Young's double slit creates two coherent sources (S₁ and S₂) from a single source using two slits.

Young's Double Slit Experiment (from Aakash PDF — Optics JEE Main):

Two slits S₁ and S₂ separated by distance d. Screen at distance D. Wavelength λ.

Path difference at point P (height y from centre): Δ = yd/D (for y << D)

Bright fringe (constructive): Δ = nλ → y_n = nλD/d (n = 0, ±1, ±2, ...)

Dark fringe (destructive): Δ = (2n–1)λ/2 → y_n = (2n–1)λD/2d

Fringe width (spacing between consecutive bright or dark fringes):

β = λD/d

β increases with λ (red fringes wider) and D; decreases with d (closer slits → wider fringes). β independent of fringe order n.

Intensity in YDSE (from Aakash PDF — Optics JEE Main):

Phase difference δ = (2π/λ) × path difference = (2π/λ) × yd/D

General resultant intensity: I = I₁ + I₂ + 2√(I₁I₂) cosδ

For equal sources (I₁ = I₂ = I₀):

I = 4I₀ cos²(δ/2)

Maximum (δ=0, 2π, 4π...): I_max = 4I₀

Minimum (δ=π, 3π...): I_min = 0

General (unequal sources): I_max = (√I₁+√I₂)²; I_min = (√I₁–√I₂)²

Effect of Medium and Other Changes (from Aakash PDF — Optics JEE Main):

In medium of refractive index n: λ_medium = λ/n → β_medium = λD/(nd) = β/n (fringes become narrower).

When source is shifted up by y_s: fringe pattern shifts DOWN by (D/d)×y_s×(d/S) where S=distance from source to slits.

Thin film (thickness t, index n) placed over one slit: path difference changes by (n–1)t; fringe pattern shifts by (n–1)t×D/d.

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Diffraction, Polarisation — Single Slit, Malus's Law, Brewster's Law

Why Single Slit First Minima a sinθ=λ, Malus's Law I=I₀cos²θ, and Brewster's Law tanθ_B=n Are Direct Optics JEE Main Questions

Single Slit Diffraction (from Aakash PDF — Optics JEE Main):

A single slit of width 'a' illuminated by wavelength λ, screen at distance D.

Condition for nth minimum (dark band): a sinθ = nλ (n = ±1, ±2, ...)

For small angles: sinθ ≈ θ = y/D → y_n = nλD/a

First minimum at y₁ = λD/a from centre.

Width of central maximum = 2λD/a = 2λf/a (from –y₁ to +y₁; twice the distance to first minimum)

Secondary maxima (approximately at a sinθ = (2n+1)λ/2). Angular half-width of central max = λ/a.

Narrower slit → wider central maximum (diffraction ∝ 1/a). Wider slit → narrower pattern → approaches geometric (ray optics) limit.

Comparison: YDSE vs Single Slit (from Aakash PDF — Optics JEE Main):

YDSE: bright at path diff = nλ (maxima). Single slit: dark at a sinθ = nλ (minima at multiples of λ).

In YDSE with single slit: missing orders where both conditions coincide.

Resolving Power (from Aakash PDF — Optics JEE Main):

Rayleigh's criterion: two point sources are just resolved when the central maximum of one falls on the first minimum of the other.

θ_min = 1.22λ/a (for circular aperture of diameter a)

Resolving power of telescope: RP = a/(1.22λ). Resolving power of microscope: RP = 2n sinα/(1.22λ) = 2 NA/λ.

Polarisation (from Aakash PDF — Optics JEE Main):

Natural light has E-field vibrating in all directions perpendicular to propagation. Polarised light has E-field vibrating in one direction only.

Polaroid: transmits light with E along its transmission axis.

Malus's Law: When polarised light (intensity I₀) passes through a polaroid at angle θ to its transmission axis:

I = I₀ cos²θ

θ=0°: I=I₀ (maximum). θ=90°: I=0 (extinction). θ=45°: I=I₀/2.

Brewster's Law (from Aakash PDF — Optics JEE Main):

When light is incident at Brewster's angle θ_B on a glass surface (refractive index n), the reflected ray is completely plane polarised:

tanθ_B = n

At Brewster's angle: reflected ray ⊥ refracted ray (angle between them = 90°).

θ_B + θ_r = 90° → θ_r = 90°–θ_B (refracted ray is partially polarised).

For glass (n=1.5): θ_B = tan⁻¹(1.5) ≈ 56°.

Natural light: after Malus's law through one polaroid → I = I₀/2 (independent of θ, since natural light has all orientations equally).

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