The lens power is +4.00 diopters. The sharp point on the card is the focal point of the lens. The distance from the lens to that point is the focal length. Here the focal length is 0.25 meter. Lens power in diopters is 1 divided by the focal length in meters. One divided by 0.25 is 4. The power is plus because a convex lens converges light.
The rule is written D = 1/F, where D is power in diopters and F is focal length in meters. Power and focal length move in opposite ways. A stronger lens has a shorter focal length. A lens that focuses at 1 meter is +1.00 D. One that focuses at 2 meters is only +0.50 D. One that focuses at 4 centimeters is a very strong +25.00 D. You must put the distance in meters, not centimeters, or the answer will be far too large. A concave, or minus, lens spreads light out instead. It forms no real point on a card, so its power is written as a negative number. Two things set the power of a lens: the curve of its surfaces and the refractive index of its material. The refractive index is a number for how much the material slows light. A more steeply curved lens of the same material bends light more. It is stronger, and its focal point sits closer.
Always change the focal distance to meters and then take one over that number. A lens that focuses at a quarter of a meter is a 4 diopter lens. The same math runs the other way. A +2.00 D lens focuses distant light at half a meter. This link between power and focal length is basic knowledge in the COA optics and spectacles content area.
Incorrect Answers
- A. This simply repeats the focal length in meters. A +0.25 D lens is very weak and would focus light 4 meters away.
- B. A +2.50 D lens brings distant light to a point at 0.40 meter, which is farther back than the card.
- D. A +25.00 D lens focuses at only 4 centimeters. That is a much shorter focal length than the one measured here.
Testing Pearls
- Lens power in diopters equals one over the focal length in meters.
- Focal length 0.50 meter gives +2.00 D; focal length 0.10 meter gives +10.00 D.
- Convex plus lenses converge light and form a real, upside-down image at the focal point.
- Concave minus lenses diverge light and have a virtual focal point in front of the lens.
- Power rises with a steeper curve and with a higher refractive index.
References
- American Academy of Ophthalmology. Ophthalmic Medical Assisting: An Independent Study Course. Chapter 5, Optics and Refractive States of the Eye.
