In optics, the power of a lens (its ability to converge or diverge light) is measured in which of the following units?

Introduction / Context:
In the study of optics and vision, lenses are described not only by their focal length but also by a quantity called power. Power indicates how strongly a lens converges or diverges light and is vital in prescribing spectacles or designing optical instruments. This question asks in which unit this power is expressed in physics and practical eye care.

Given Data / Assumptions:

• The physical quantity under discussion is the power of a lens.

• The options include dioptres, aeon, lumen, candela and watt.

• The learner is expected to know the relationship between power and focal length.

• Basic optics concepts from school level physics are assumed.

Concept / Approach:
The power P of a lens in optics is defined as the reciprocal of its focal length f when f is expressed in metres, so P = 1 / f. The SI unit that corresponds to this reciprocal metre is called the dioptre (often spelled diopter). For example, a lens with focal length 0.5 metre has a power of 2 dioptres. The other units listed are used for different physical quantities related to light, such as luminous flux and luminous intensity, not for lens power.

Step-by-Step Solution:
Step 1: Recall the formula for lens power: P = 1 / f, where f is in metres. Step 2: Understand that this means the unit of power is reciprocal metre, written as m⁻¹. Step 3: Recognise that the special name given to this unit in optics is the dioptre. Step 4: Look at the options and identify dioptres (diopters) as the one that matches this concept. Step 5: Select dioptres (diopters) as the correct answer.

Verification / Alternative check:
Physics textbooks, especially chapters on refraction and eye defects, consistently state that lens power is measured in dioptres. Prescription values on eyeglasses are labelled with a number followed by the letter D, indicating dioptres. In contrast, lumen and candela are photometric units for luminous flux and luminous intensity respectively, and watt measures electrical or radiant power in energy per unit time. No reputable optics reference uses these units for lens power, confirming that dioptres is correct.

Why Other Options Are Wrong:
Aeon is not a standard physics unit for this context. Lumen measures the total amount of visible light emitted by a source per unit time, and candela measures how bright a source appears in a particular direction. Watt is a unit of power in mechanics and electricity, not optical lens power. None of these describe the reciprocal of focal length or are used in spectacle prescriptions, so they are not suitable answers.

Common Pitfalls:
Some candidates confuse the everyday word power with electrical power and may be tempted to choose watt. Others see light related units like lumen and candela and think they must be connected to lenses. To avoid mistakes, remember that lens power is geometrical and depends on curvature and refractive index, not on brightness or electrical energy. The special name dioptre was introduced specifically for this reciprocal metre quantity and is widely used in eye care.

Final Answer:
The power of a lens is measured in dioptres (diopters).