An object with a height of 16 cm is located at a distance of 80 cm from a diffusing lens

An object with a height of 16 cm is located at a distance of 80 cm from a diffusing lens with an optical power of -2.5 diopters. How many times will the image height change if the object is moved 40 cm to the lens?

From the formula for the optical power, we express the focus, it is equal to the ratio 1 / -2.5 = -0.4 (m).
Let’s use the converging lens formula 1 / F = 1 / d + 1 / f. Consider two situations. In the first d = 0.8 (m), in the second – 0.4 (m). 1) -2.5 = 1 / 0.8 + 1 / f. Let’s substitute additional factors and express f: f = -4 / 15 (since this is a distance, minus does not matter). 2) -2.5 = 1 / 0.4 + 1 / f. Substitute and express: f = -1 / 5 = -0.2 (m) (minus is always obtained, does not affect the course of the solution). Now we find the ratio of sizes relative to each other: (1/5) / (4/15) = 1/5 * 15/4 = 3.4. Substituting and calculating, we find that the size will decrease by 1.33 times (4/3).