PhysicsOpticsJEE Main & Advanced

Optics Formulas

Complete chapter-wise formula sheet for Optics (Physics) covering key equations, parameters, traps, and concept diagrams for JEE Main & Advanced.

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Chapter Directory (24 Chapters)

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Optics698 Qs

Ray Optics & Optical Instruments

Snell's law, total internal reflection, lens maker's formula, thin lenses, prism formula, and microscopes/telescopes.

11 Formulas Diagram

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Optics578 Qs

Wave Optics & Interference

Huygens principle, Young's Double Slit Experiment (YDSE), single slit diffraction, and polarization Brewster law.

8 Formulas Diagram

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Formulas Reference (Optics)

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OpticsTop Priority (3-4 Qs in JEE)698 PYQs

Ray Optics & Optical Instruments

Snell's law, total internal reflection, lens maker's formula, thin lenses, prism formula, and microscopes/telescopes.

Chapter

Mirror & Thin Lens Formulas

\frac{1}{f} = \frac{1}{v} + \frac{1}{u} \; (\text{Mirror}), \quad \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \; (\text{Lens}), \quad m = -\frac{v}{u} \; (\text{Mirror}), \quad m = \frac{v}{u} \; (\text{Lens})

Fundamental imaging equations with focal length and lateral magnification.

Always substitute numerical values with their proper algebraic signs.

Snell's Law & Total Internal Reflection (TIR)

n_1 \sin i = n_2 \sin r, \quad \sin\theta_c = \frac{n_2}{n_1} = \frac{1}{\mu}

Law of refraction and critical angle condition for TIR (light traveling from denser to rarer medium).

Optical fiber core refractive index must be greater than cladding (n_core > n_cladding).

Lens Maker's Formula

\frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right), \quad P = \frac{1}{f \text{ (in meters)}}

Determines focal length from glass refractive index and surface curvature radii.

Immersing a glass lens in water increases its focal length by roughly a factor of 4.

Prism Formula (Minimum Deviation)

A + \delta = i + e, \quad \mu = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)}

Connects prism angle A, angle of minimum deviation δ_m, and refractive index μ.

At minimum deviation: i = e and r₁ = r₂ = A/2.

Compound Microscope & Astronomical Telescope

m_{\text{microscope}} = -\frac{v_o}{u_o}\left(1 + \frac{D}{f_e}\right), \quad m_{\text{telescope}} = -\frac{f_o}{f_e}, \quad L_{\text{telescope}} = f_o + f_e

Magnifying power for visual optical instruments at normal adjustment.

D = least distance of distinct vision = 25 cm.

Refraction at Spherical Curved Surface

\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}, \quad m = \frac{\mu_1 v}{\mu_2 u}

General Gaussian refraction formula at curved dielectric boundary separating media μ₁ and μ₂.

Apparent depth for flat boundary (R → ∞): d' = d / (μ₁/μ₂) = d / μ_rel.

Silvering of Lenses (Equivalent Curved Mirror)

\frac{1}{F_{\text{eq}}} = \frac{2}{f_l} + \frac{1}{f_m} \implies P_{\text{eq}} = 2P_l + P_m

A silvered thin lens acts as a concave or convex mirror. Light passes through lens twice and reflects once.

Plano-convex lens silvered on flat face acts as concave mirror of focal length F = R / (2(μ - 1)).

Normal Shift by Glass Slab & Lens Cutting Rules

\Delta t = t\left(1 - \frac{1}{\mu}\right), \quad \text{Cut Along Axis: } f' = f, \; I' = \frac{I}{2}, \quad \text{Cut Perpendicular to Axis: } f' = 2f

Apparent shift in object position caused by flat slab of thickness t, and changes in focal length and image brightness upon lens division.

Separated thin lenses: 1/F = 1/f₁ + 1/f₂ - d/(f₁ f₂).

Power of Lens Combination (In Contact & Separated)

P_{\text{contact}} = P_1 + P_2, \quad P_{\text{separated}} = P_1 + P_2 - d \cdot P_1 P_2, \quad f_{\text{separated}} = f_1 + f_2 - \frac{d}{\text{...}} \implies \frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2} - \frac{d}{f_1 f_2}

Equivalent focal length and power of two thin lenses separated by distance d (measured between optical centres). In contact: d = 0, so P = P₁ + P₂.

Achromatic doublet condition (no chromatic aberration): ω₁/f₁ + ω₂/f₂ = 0, giving f₁ω₂ + f₂ω₁ = 0. Both lenses must have opposite signs of focal length.

Chromatic Aberration & Dispersive Power

\omega = \frac{\mu_V - \mu_R}{\mu_Y - 1} = \frac{f_R - f_V}{f_Y}, \quad \text{Chromatic aberration} = f_R - f_V = \omega f_Y

Dispersive power ω measures how much a lens separates different colours of light. μ_V, μ_R, μ_Y are refractive indices for violet, red, and yellow light respectively.

Crown glass: ω ≈ 0.016 (low dispersion); Flint glass: ω ≈ 0.033 (high dispersion). Achromatic doublet uses crown + flint to cancel chromatic aberration.

Optical Instruments — Microscope & Telescope

m_{\text{micro}} = -\frac{v_o}{u_o}\left(1 + \frac{D}{f_e}\right), \quad m_{\text{tele}} = -\frac{f_o}{f_e}\left(1 + \frac{f_e}{D}\right), \quad L_{\text{tele}} = f_o + f_e \; (\text{normal})

Magnifying power and tube length for compound microscope and astronomical refracting telescope. For relaxed eye (image at infinity): m_micro ≈ -(L/f_o)(D/f_e) and m_tele = -f_o/f_e.

Resolving power of telescope: RP = D_aperture / (1.22 λ). Resolving power of microscope: RP = 2μ sin θ / (1.22 λ), where μ sin θ is numerical aperture.

OpticsHigh Yield (2-3 Qs in JEE)578 PYQs

Wave Optics & Interference

Huygens principle, Young's Double Slit Experiment (YDSE), single slit diffraction, and polarization Brewster law.

Chapter

Superposition of Two Waves (Interference)

I = I_1 + I_2 + 2\sqrt{I_1 I_2}\cos\phi, \quad I_{\text{max}} = (\sqrt{I_1} + \sqrt{I_2})^2, \quad I_{\text{min}} = (\sqrt{I_1} - \sqrt{I_2})^2

Resultant intensity of two coherent wave sources with phase difference φ.

If sources are identical (I₁ = I₂ = I₀): I = 4 I₀ cos²(φ/2).

Young's Double Slit Experiment (YDSE)

\beta = \frac{\lambda D}{d}, \quad y_n = n \frac{\lambda D}{d} \; (\text{Bright}), \quad y_n = \left(n - \frac{1}{2}\right)\frac{\lambda D}{d} \; (\text{Dark})

Fringe width β, slit separation d, and screen distance D.

Immersing YDSE in liquid of index μ compresses fringe width to β/μ.

Fringe Shift by Thin Transparent Sheet

\Delta y = \frac{D}{d}(\mu - 1)t = \frac{(\mu - 1)t}{\lambda}\beta

Lateral displacement of the whole fringe pattern when mica/glass sheet of thickness t is inserted.

Number of fringes shifted is N = (μ - 1)t / λ.

Single Slit Diffraction

a\sin\theta = n\lambda \; (\text{Minima}), \quad \text{Central Maximum Angular Width } = \frac{2\lambda}{a}, \quad W = \frac{2\lambda D}{a}

Fraunhofer diffraction minima condition and central diffraction spread.

Width of central maximum is TWICE the width of secondary maxima.

Polarization (Brewster's Law & Malus' Law)

\tan i_p = \mu, \quad I = I_0 \cos^2\theta

Polarizing angle where reflected and refracted rays are perpendicular, and transmitted intensity through analyzer.

When unpolarized light passes through ideal polarizer, intensity drops to I₀/2.

Resolving Power of Telescope & Microscope (Rayleigh)

\text{RP}_{\text{telescope}} = \frac{a}{1.22\lambda}, \quad \text{RP}_{\text{microscope}} = \frac{2\mu\sin\theta}{1.22\lambda} = \frac{2\,\text{NA}}{1.22\lambda}

Limit of resolution based on diffraction Airy disc overlap. a is aperture diameter; NA is numerical aperture.

Oil immersion objectives increase μ, thereby increasing resolving power of microscope.

Fresnel Distance (Ray vs Wave Optics Boundary)

Z_F = \frac{a^2}{\lambda}, \quad \text{Ray Optics valid for } D \ll Z_F, \; \text{Diffraction dominates for } D \gg Z_F

Distance beyond which ray of light spreads by an amount comparable to aperture size a.

Diffraction spread is equal to aperture size a exactly when D = Z_F.

Thin Film Interference & Phase Shift on Reflection

2\mu t \cos r = \left(n + \frac{1}{2}\right)\lambda \; (\text{Reflected Maxima}), \quad 2\mu t \cos r = n\lambda \; (\text{Reflected Minima})

Interference in reflected rays from thin dielectric film of thickness t. Extra λ/2 path shift occurs upon reflection from denser boundary (Stokes' relation).

An extremely thin soap film (t << λ) appears completely dark in reflected light.