Determine the optical power of the converging lens if the distance from the lens to the object

Determine the optical power of the converging lens if the distance from the lens to the object is 10 cm, and the distance from the lens to the image is 25 cm.

Since the optical power of the lens D is found as the reciprocal of the focal length F of the lens: D = 1 / F, it is necessary to first calculate its focal length. To do this, we use the thin lens formula: 1 / F = 1 / d + 1 / f, where d is the distance from the lens to the object, f is the distance from the lens to the image of the object. From the condition of the problem it is known that the distance from the lens to the object is d = 10 cm = 0.1 m, and the distance from the lens to the image is f = 25 cm = 0.25 m. In addition, the condition says that the lens is collecting, this means that in the formula F> 0 and f> 0. Let’s combine the formulas: D = 1 / d + 1 / f. Let’s substitute the values ​​of physical quantities into the calculation formula and make calculations: D = 1 / 0.1 + 1 / 0.25; D = 10 + 4; D = 14 diopters.
Answer: The optical power of the collecting lens is 14 diopters.