# The subject is placed 25 cm from the front focus of the collecting lens.

The subject is placed 25 cm from the front focus of the collecting lens. The subject is captured at a distance of 36 cm behind the back focus. Determine the focal length of the lens.

Let’s start by writing a short statement of the problem.

Given:

x1 = 25 cm = 0.25 m;

x2 = 36 cm = 0.36 m.

To find:

F -?

To solve the problem, we apply the thin lens formula:

1 / F = 1 / a + 1 / b.

where F is the focal length, m;

Let a = F + x1 and b = F + x2;

We express from the formula F and substitute a and b and get:

F = ((F + x1) * (F + x2)) / (2 * F + x1 + x2);

2 * F ^ 2 + F * x1 + F * x2 = F ^ 2 + F * x1 + F * x2 + x1 * x2;

F ^ 2 = x1 * x2;

it remains to substitute the values into the formula and calculate:

x1 = 0.25;

x2 = 0.36;

F = (0.25 * 0.36) ^ 0.5 = 0.3.

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