Power of a Lens and Combination of Lenses: Easy Exam Guide

Power of a lens tells how strongly it bends light. Opticians prescribe power instead of focal length because it adds up simply when lenses are combined. Knowing power makes spectacle calculations and exam problems much faster.

When you wear glasses marked plus 2 dioptres or minus 1.5 dioptres, that number is the lens power. Combining lenses — like a camera zoom or a microscope — obeys equally simple addition rules.

Key Concepts

Power P: Reciprocal of focal length in metres, P = 1 divided by f (in metres). Unit is dioptre (D), 1 D = 1 per metre.

Sign: Convex (converging) lens positive power, concave (diverging) negative. Example +2 D means f = +0.5 m.

Combination: Two thin lenses in contact act as one lens whose power is sum of individual powers.

• Short focal length means high power and strong bending
• Plane glass has zero power, f infinite
• Power depends on medium; lens in water has less power than in air

Formulas

P = 1 divided by f (metres). f in metres, P in dioptres. If f given in centimetres, convert: f(m) = f(cm) divided by 100.

P_total = P1 + P2 + P3 + continuing terms for thin lenses in contact. Also 1 divided by F = 1 divided by f1 + 1 divided by f2 for effective focal length F. Assumes lenses thin and in contact, same medium.

For lenses separated by distance, formula is more complex, but school level mainly uses contact case.

Worked Example

A convex lens of focal length 25 cm is placed in contact with a concave lens of focal length 40 cm. Find combined power and focal length and nature.

1. Convert: f1 = +25 cm = +0.25 m, so P1 = 1 divided by 0.25 = +4.0 D.
2. f2 = minus 40 cm = minus 0.40 m, P2 = 1 divided by minus 0.40 = minus 2.5 D.
3. P_total = 4.0 minus 2.5 = +1.5 D.
4. Effective f = 1 divided by 1.5 = 0.67 m = 67 cm, positive, so combination is converging.

Even though one lens diverges, the stronger convex wins. This is how spectacle combinations tune net power.

Common Misconceptions

• Power adds by focal lengths directly: It is powers that add in contact, not focal lengths. Adding f values would give wrong result.
• Negative power means weaker: Magnitude shows strength. Minus 4 D bends as strongly as plus 4 D, just diverging instead.
• Power zero means no lens: A combination can cancel to zero, acting like plane glass, even though lenses present.

Real-World Applications

• Opticians prescribe spectacle power in dioptres for accurate vision correction
• Combination in microscopes (objective plus eyepiece) yields high total magnification
• Camera zoom lenses vary effective power by moving lens groups
• Phoropters in eye clinics combine lenses quickly to find patient prescription

Power P = 1 divided by f (metres) in dioptres summarises lens strength. For lenses in contact powers simply add, giving combined focal length immediately.