The collecting lens gives an actual image of the object magnified by 2.5

The collecting lens gives an actual image of the object magnified by 2.5 times. if the distance from the object to the lens is 70 cm, then its optical power is …

Solution.
Replace in the thin lens formula: 1 / F = 1 / d + 1 / f, where F is the focal length of the lens, d is the distance from the object to the lens, f is the distance from the image to the lens obtained with this lens, 1 / F on D, since the optical power of the lens is D = 1 / F. We also replace f with G ∙ d, since the magnification of the lens is G = f / d. We get, 1 / d + 1 / (Г ∙ d) = D, then D = (Г + 1) / (Г ∙ d). From the condition of the problem it is known that the collecting lens gives a real image of the object magnified by G = 2.5 times, and the distance from the object to the lens is d = 70 cm = 0.7 m. Substitute the values ​​of physical quantities into the formula and perform calculations to find optical power of the lens:
D = (2.5 + 1) / (2.5 ∙ 0.7);
D = 2 diopters.
Answer: The optical power of the lens is 2 diopters.