# 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)