Lens Formula

• Lens formula: 1/f = 1/v − 1/u (NCERT sign convention).
• Magnification m = h′/h = v/u.
• Power of lens P = 1/f (f in metres); unit dioptre (D).
• Combination of thin lenses in contact: 1/F = 1/f₁ + 1/f₂.
• Numerical problems on image distance, magnification, and power.

1. Lens formula — 1/f = 1/v − 1/u; valid for thin lenses, paraxial rays.
2. Sign convention — u negative for real object; v positive for real image; f positive for convex, negative for concave.
3. Magnification — m = v/u; m > 0 erect, m < 0 inverted; |m| gives size ratio.
4. Power — P = 1/f (m); +P converging, −P diverging.
5. Combined lenses — P_total = P₁ + P₂ for lenses in contact.
6. Real image — v positive; forms on opposite side of lens from object.
7. Virtual image — v negative; same side as object.
8. Example — lens +2.0 D has f = 0.5 m = 50 cm (convex).
9. SI unit — dioptre = m⁻¹.
10. NCERT numerical style — always list u, f with signs before substitution.

Find image distance: convex lens f = +20 cm, object at u = −30 cm

Given: f = +20 cm, u = −30 cm
Step 1 — 1/f = 1/v − 1/u → 1/20 = 1/v − 1/(−30)
Step 2 — 1/v = 1/20 − 1/30 = (3−2)/60 = 1/60
Step 3 — v = +60 cm (real image beyond 2F)
Step 4 — m = v/u = 60/(−30) = −2 → inverted, twice size
Step 5 — Check: object beyond 2F → diminished? Wait: u=30, f=20 → object between F and 2F → enlarged. m=−2 confirms enlarged.
Conclusion: real, inverted, magnified image at 60 cm.

• Using mirror formula 1/f = 1/v + 1/u for lenses.
• Forgetting to convert f to metres when calculating power.
• Sign error on u (must be negative for real object).
• Misconception: magnification always positive.
• Adding focal lengths instead of powers for combined lenses.

• Write lens formula and magnification formula.
• A lens has power +2.5 D. Find focal length.
• If u = −15 cm and v = +30 cm, find f.
• What does negative magnification indicate?

Open the Practice tab for graded questions on Lens Formula.