Refraction and Lenses: JEE Main Deep Dive

Refraction and lenses constitute the more demanding half of JEE Main optics, typically contributing 1–2 questions per session. The chapter spans Snell's law, critical angle, total internal reflection, refraction at spherical surfaces, thin lens formula, lens maker's equation, and combination of lenses. Understanding the Cartesian sign convention is absolutely non-negotiable — the single largest source of errors in optics problems is sign confusion. This guide systematically covers every subtopic with the precision required to solve any JEE Main refraction problem in under 3 minutes.

Snell's Law, Refraction, and Critical Angle

Snell's law: n1·sin(i) = n2·sin(r). When light travels from denser to rarer medium (n1 greater than n2), the refracted ray bends away from the normal. At the critical angle theta_c, sin(theta_c) = n2/n1, and r = 90°. Beyond theta_c, total internal reflection (TIR) occurs — used in optical fibre technology. JEE Main loves TIR problems involving prisms and optical fibres. For a glass-air interface with n_glass = 1.5, theta_c = arcsin(2/3) approximately 41.8°. Apparent depth formula: apparent depth = real depth / n (for normal incidence). When the object is in the denser medium and observer in air, the image appears closer. This is tested with layered media (multiple refracting layers), where you add the apparent depths for each layer. For related optics topics, see our comprehensive Ray and Wave Optics Guide that covers mirrors, interference, and diffraction alongside refraction.

Refraction through a glass slab: for a parallel-sided slab of thickness t and refractive index n, the emergent ray is parallel to the incident ray but laterally displaced. Lateral shift d = t·sin(i−r)/cos(r). This formula appears in JEE Main directly. Also know: when an object in a medium of refractive index n1 is seen through a flat interface into medium n2, the object appears to shift. For n1 = 1.5 (glass) and n2 = 1 (air), a fish 60 cm deep appears at 40 cm depth.

Refraction at Spherical Surfaces and Lenses

Refraction at a single spherical surface: n1/v − n2/u = (n1−n2)/R. (Wait — the standard form is n2/v − n1/u = (n2−n1)/R using Cartesian sign convention with incident light going left to right, all distances measured from the pole.) Apply this to a glass sphere, a curved glass-water interface, or a plano-convex lens surface. For a thin lens, apply refraction at each surface and combine: 1/f = (n−1)[1/R1 − 1/R2] — the lens maker's equation. Sign convention: R is positive for a centre of curvature to the right of the surface. Convex lens has f positive; concave lens has f negative. Practice JEE Main mock tests with optics problems to drill the sign convention until it becomes automatic.

The thin lens formula: 1/v − 1/u = 1/f (Cartesian). Magnification m = v/u for a single lens. For real images (formed on the other side of the lens from the object), v is positive and m is negative — image is inverted. Virtual images (u between 0 and −f for convex lens) give positive v and positive m — image is erect and magnified. Lens power P = 1/f (in dioptres, with f in metres). For two thin lenses in contact: P_total = P1 + P2, or 1/f_eff = 1/f1 + 1/f2. For lenses separated by distance d: 1/f_eff = 1/f1 + 1/f2 − d/(f1·f2).

Prisms: Deviation and Dispersion

A prism of apex angle A and refractive index n deviates light by angle delta = i + e − A, where i is angle of incidence and e is angle of emergence. At minimum deviation D_m, i = e and the ray passes symmetrically: sin((A+D_m)/2) = n·sin(A/2). JEE Main frequently asks: given n and A, find D_m, or vice versa. Dispersion: a prism splits white light because n varies with wavelength (n_violet greater than n_red). Angular dispersion = delta_v − delta_r = (n_v − n_r)·(A for small angles). Dispersive power omega = (n_v − n_r)/(n_mean − 1). Achromatic doublet: two prisms with omega1·P1 + omega2·P2 = 0 (no net dispersion). Direct vision prism: net deviation = 0 but dispersion retained. These results appear in JEE Main more often than students expect.

For a prism at minimum deviation, using i = e implies the refracted ray inside the prism is parallel to the base. You can derive n = sin((A+D_m)/2)/sin(A/2) without memorisation by applying Snell's law at both surfaces and using geometry. Derive this formula once from scratch — it builds geometric insight and ensures you can reconstruct it if you forget it under exam pressure.

Optical Instruments: Microscope and Telescope

The simple microscope (magnifying glass) gives magnification M = 1 + D/f (near point formula) or M = D/f (far point / relaxed eye). For a compound microscope, M = L/f_o × D/f_e where L is the tube length (distance between rear focal point of objective and front focal point of eyepiece). For an astronomical telescope in normal adjustment: M = f_o/f_e, tube length = f_o + f_e. These formulas appear verbatim in JEE Main questions. Register on our platform to access 250+ optics problems including refraction, lenses, and optical instruments. See our pricing for full test series access. For numerical problem-solving practice in optics, our Optics Numericals Guide provides step-by-step solutions to the 50 most commonly tested numerical types.

In JEE Main, lens and refraction problems are best handled by committing to the Cartesian sign convention strictly, sketching a ray diagram (even a rough one) for context, and applying the relevant formula with careful sign substitution. A 30-second diagram saves 2 minutes of algebraic confusion in nearly every optics problem.