An object with a height of 2 cm is located 15 cm from the collecting lens with an optical power of 10 diopters.

An object with a height of 2 cm is located 15 cm from the collecting lens with an optical power of 10 diopters. Find the height of the image and the distance from it to the lens.

Given:
d = 15cm = 0.15m,
h = 2cm = 0.02m,
D = 10dvr;
To find:
f and H -?
Let’s write down the basic lens formula:
1 / f + 1 / d = 1 / F,
where
F = 1 / D = 0.1m – lens focal length;
From the formula, we find the distance of the image to the lens:
f = d * F / (d – F) = 0.3m;
The magnification of the lens (the ratio of image size to object size) is determined from the formula:
H / h = f / d;
H = h * (f / d) = 0.02 * 2 = 0.04m = 4cm.