Questions: Lens Power and Dioptric Strength

Question 1

A convex lens has a focal length of 0.25 m. What is its optical power, and what does that value mean?

• A. 0.25 D — power equals focal length in meters
• B. 4 D — it can bring parallel light to a focus four times more strongly than a 1-meter lens
• C. 4 D — it has four times the refractive index of air
• D. 0.25 D — shorter focal lengths mean weaker lenses

Answer: (B)

P = 1/f = 1/0.25 = 4 D. A diopter is an inverse meter, so 4 D means the lens converges light four times as strongly as a lens with f = 1 m. Option D inverts the relationship: a shorter focal length means *more* power, not less, because a lens that focuses light in a short distance must bend it more sharply.

Question 2

An ophthalmologist prescribes corrective lenses: a −2.0 D lens in contact with a +3.5 D lens. What is the combined power?

• A. −7.0 D — the powers multiply when lenses are in contact
• B. +1.5 D — powers of thin lenses in contact add directly
• C. Cannot be determined without knowing the focal lengths separately
• D. +5.5 D — you add the absolute values and keep the sign of the stronger lens

Answer: (B)

The key advantage of the diopter system is that powers of thin lenses in contact add algebraically: P_total = P₁ + P₂ = −2.0 + 3.5 = +1.5 D. This is why opticians and ophthalmologists work in diopters rather than focal lengths — combining focal lengths requires the more complex formula 1/f = 1/f₁ + 1/f₂, while powers simply add. Option A confuses multiplication (used for magnification) with the additive rule for power.

Question 3

A diverging (concave) lens has negative optical power.

• T. True
• F. False

Answer: True

A diverging lens spreads light outward rather than converging it, so it has a negative focal length by sign convention. Since P = 1/f, negative f gives negative P. An eyeglass prescription of −1.75 D corrects nearsightedness by adding diverging power that spreads light slightly before it enters the eye, allowing the eye's own optics to focus it correctly on the retina.

Question 4

A lens with a shorter focal length has less optical power because it bends light through a smaller angle.

• T. True
• F. False

Answer: False

This inverts the relationship. A shorter focal length means a *more* powerful lens, because P = 1/f — as f decreases, P increases. A lens that focuses parallel light to a point 10 cm away (f = 0.1 m, P = 10 D) bends light far more sharply than one that focuses it 100 cm away (f = 1 m, P = 1 D). The confusion arises from thinking of 'distance' as magnitude of effect — but in optics, shorter distance to focus means stronger bending.

Question 5

Why is optical power defined as the reciprocal of focal length (P = 1/f) rather than using focal length directly as the measure of lens strength?

Model answer: Because power is additive: when thin lenses are placed in contact, their powers add directly (P_total = P₁ + P₂), making optical system design simple arithmetic. Focal lengths do not add this way. Power also scales intuitively with strength — a stronger lens (shorter f) has higher P — whereas focal length scales inversely.

The additive property of power is the core engineering motivation. Camera lenses, telescopes, microscopes, and the human eye all involve multiple refracting surfaces working in series. Expressing each surface's contribution in diopters lets designers sum them to find the total focusing strength. The lensmaker's equation extends this: each surface of a single lens contributes its own power based on its radius of curvature and refractive index, and those contributions add to give the lens's total power.