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

July 26, 2021 | education

| **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.

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