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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