The lamp is located 20cm from the collecting lens, what is the power of the optical power

The lamp is located 20cm from the collecting lens, what is the power of the optical power of the lens if the actual image of the lamp is at a distance of 25cm from the lens?

The optical power of the lens D is found as the reciprocal of the focal length F of the lens: D = 1 / F. And the focal length can be determined using 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. Combining the formulas, we get: D = 1 / d + 1 / f. From the condition of the problem it is known that the lamp is at a distance d = 20 cm = 0.2 m from the collecting lens, and the actual image of the lamp is at a distance f = 25 cm = 0.25 m from the lens. Let’s substitute the values ​​of physical quantities into the calculation formula and make calculations: D = 1 / 0.2 + 1 / 0.25; D = 5 + 4; D = 9 diopters.
Answer: The optical power of the lens is 9 diopters.