Lens Maker's FormulaJEE Main

Grind two surfaces, get a focal length — interactive Physics simulation for IIT-JEE.

Concept

The lens maker's formula predicts focal length from the two surface curvatures and the index contrast between lens and surroundings. A glass lens converges in air but weakens ~4× in water — and a lens made of n lower than its medium flips behaviour entirely (an air bubble in water diverges).

Key formula

\frac{1}{f} = \left(\frac{n_{lens}}{n_{medium}} - 1\right)\left(\frac{1}{R_1} - \frac{1}{R_2}\right), \qquad P = \frac{1}{f\,(\text{in m})}

Derivation

Refraction at a single spherical surface: $\frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2-n_1}{R}$ . Apply it at the front surface, feed that image as the object for the back surface (thin lens ⇒ same position), and add:

the intermediate terms cancel, leaving the lens maker's formula. Sign convention: distances measured from the lens, positive along the light's travel.

Scenarios to explore

Lens Maker's Formula — Curvatures + index contrast → focal length & power.

Real-world applications

Spectacle prescription in dioptres.
Camera lens design; achromatic doublets pair crown & flint glass.
The eye: cornea + adjustable crystalline lens.

JEE exam tips

Biconvex with |R₁| = |R₂| = R and n = 1.5 ⇒ f = R. One-second answer.
Glass lens (1.5) in water (1.33): f multiplies by about 4.
Silvered lens = lens + mirror + lens: P = 2P_lens + P_mirror.

Common mistakes

Sign errors on R₁/R₂ — draw the lens, mark each centre of curvature.
Using (n − 1) in a medium other than air (need n_rel = n_lens/n_med − 1).
Power in dioptres with f in cm — convert to metres.

Exam traps to avoid

n_medium > n_lens flips converging ↔ diverging.
Plano surfaces have R = ∞ — the 1/R term just drops.