9.3.8. Power of a Lens

You have already learnt that the ability of a lens to converge or diverge light rays depends on its focal length. For example, a convex lens of short focal length bends the light rays through large angles, by focussing them closer to the optical centre. Similarly, concave lens of very short focal length causes higher divergence than the one with longer focal length.

The power of a lens indicates how effectively it can bend light. A lens with a short focal length can bend light more sharply than a lens with a longer focal length. This means that close objects can be brought into focus more easily with a high power lens, enhancing the vision effectively.

Think of a water hose with a nozzle. If the nozzle is narrow, the water shoots out with more force, similar to how a lens with a short focal length focuses light sharply. If the nozzle is wider, the water spreads out and loses force, much like a lens with a longer focal length that produces a less focused image.

The degree of convergence or divergence of light rays achieved by a lens is expressed in terms of its power. The power of a lens is defined as the reciprocal of its focal length. It is represented by the letter P. The power P of a lens of focal length f is given by

1 P = (9.11) f

The power of a lens (P) is calculated by taking the reciprocal of the focal length (f) measured in meters. This relationship means that as the focal length decreases (meaning the lens bends light more), the power increases. For example, a lens with a focal length of 0.5 meters has a power of 2 diopters, which indicates it will bend light sharply, assisting with tasks such as reading.

If you think of a magnifying glass, a lens with a shorter focal length is like a very short straw. If you try to drink with it, you’ll get a strong, quick rush of juice, just as a short focal length lens gives a strong bend to the light rays. In contrast, using a long straw (a longer focal length) means the drink flows more gently.

The SI unit of power of a lens is ‘dioptre’. It is denoted by the letter D. If f is expressed in metres, then, power is expressed in dioptres. Thus, 1 dioptre is the power of a lens whose focal length is 1 metre. 1D = 1m–1.

Power is quantified in diopters, where 1 diopter corresponds to a lens with a focal length of 1 meter. This unit simplifies how we express the capacity of lenses in optics, aiding in better understanding when selecting lenses for vision correction and other applications.

Imagine you’re biking down a hill. If you have a steep track (like a strong lens with a short focal length), you’ll gain speed quickly. If the hill is shallow (like a long focal length lens), the speed builds more slowly. In both cases, the steepness or shallowness directly correlates with how quickly you react to a road ahead, akin to how quickly a lens will focus light.

You may note that the power of a convex lens is positive and that of a concave lens is negative.

Convex lenses converge light and are represented by positive power values, while concave lenses cause light to diverge, thus having negative power values. This distinction is important in fields like optometry, where the lens type determines how effectively it corrects vision.

Think of a magnifying glass as a friend that brings things closer to you (positive, like a convex lens), helping you see things you couldn’t before. Now, think of a magnifying glass turned the other way, one that spreads out the light, making distant objects seem even further away (negative, like a concave lens) — this doesn’t help much for looking up close!

Opticians prescribe corrective lenses indicating their powers. Let us say the lens prescribed has power equal to + 2.0 D. This means the lens prescribed is convex. The focal length of the lens is + 0.50 m. Similarly, a lens of power – 2.5 D has a focal length of – 0.40 m. The lens is concave.

When visiting an optician, the power of corrective lenses is crucial for adjusting vision. A positive power indicates a lens that brings light together for better focus on nearby objects (typically aiding those with farsightedness). Conversely, a negative power suggests it’s for correcting nearsightedness, helping bring distant objects into view.

Imagine you’re reading a book but can’t see the words clearly. The optician provides lenses based on the ‘power’ of your eyesight, much like using different tools in a toolbox. A pair of binoculars may help you focus on something far away (like convex lenses), whereas a magnifier helps you see tiny details up close (like concave lenses).

Many optical instruments consist of a number of lenses. They are combined to increase the magnification and sharpness of the image. The net power (P) of the lenses placed in contact is given by the algebraic sum of the individual powers P , P , P , … as

P = P + P + P + …

In devices like cameras, microscopes, and telescopes, multiple lenses are used together to enhance image quality. The total power of all the lenses combined is simply the sum of their individual powers, allowing for greater functionality and versatility in optical devices.

Think of a team of players in basketball. Each player's strengths contribute to the team's overall performance. Similarly, when lenses work together, their combined power helps to create clearer, sharper images, just like teamwork leads to better results on the court.

--