You are given three lenses L1, L2, and L3, each of focal length 20cm. An object is kept at 40cm in front of L1. The final real image is formed at the focus of L3. Find the separations between L1, L2, and L3.

The separations between the lenses will be as follows:
Distance between L2 and L3 doesn't matter as the image formed by L2 is at infinity so that X2 can take any value. Image by L3 is formed at the focus. So the object should lie at infinity for L3. So, L2 will form an image at infinity and the object for L2 should be at its focus. But we have seen above that the image by L1 is formed at 40cm right of L1 which is at 20cm left of L2. So, Distance between L1 and L2 = 20 + 40 = 60cm