OpticsTop Priority (3-4 Qs in JEE)

Ray Optics & Optical Instruments Formulas

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

11 Formulas•698+ Questions in Bank•

Concept Diagram

Convex Lens Real Image Formation

Ray tracing through thin biconvex lens showing object at >2F, focal points F and 2F, and real inverted diminished image.

Core Formulas & Mathematical Identities

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})

Diagram Reference:Mirror & Thin Lens Formulas

Fundamental imaging equations with focal length and lateral magnification.

Examiner Tip: 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).

Examiner Tip: 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.

Examiner Tip: 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.

Examiner Tip: 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.

Examiner Tip: 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.

Examiner Tip: 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.

Examiner Tip: 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.

Examiner Tip: 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.

Examiner Tip: 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.

Examiner Tip: 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.

Examiner Tip: 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.

Top Examiner Traps & Pitfalls

Frequently tested misconceptions in Ray Optics & Optical Instruments

•Cartesian sign convention mistakes: measuring distances against light propagation direction must be NEGATIVE.
•Focal length of convex lens is POSITIVE, concave lens is NEGATIVE.

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