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

August 18, 2021 | education

| **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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