# Determine the focal length of the collecting lens if the distance between the virtual image of the object and the lens

Determine the focal length of the collecting lens if the distance between the virtual image of the object and the lens is f = 90 cm. It is known that the lens gives an increase of G = 4.

Let’s start to disassemble everything from the very beginning. We were given a lens magnification, which is why we can use this for our own purposes, that is, to find the value of f. So, let’s write a forum that will allow us to express f: D = f / d from it. D is a known value, we will express from the formula f, it is equal to 4D. Now let’s remember the formula for a thin lens: 1 / F = 1 / d + 1 / f. Let’s substitute additional factors and express the focus from here: F = d * f / f-d. Let’s substitute: F = f / 4 * f / f-f / 4 = 22.5 * 90 / 90-22.5 = 22.5 * 90 / 67.5 = 30 (cm).
Let us express in basic units: 0.3 (m)

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