Find the position of the image formed by the lens combination given in the figure.

Explanation

Image formed by the fist lens `(1)/(v_(1)) -(1)/(u_(1)) = (1)/(f_(1))`
`(1)/(v_(1)) - (1)/(-30) = (1)/(10) or v_(1) = 15 cm `
The image formed by the first lens serves as the object for the second. This is at a distance of (15 -5) cm = 10 cm to the right of the second lens. though the image is real, it serves as a virtual object for the second lens, Which means that the rays appear to come from it for the second lens.
`(1)/(v_(2)) - (1)/(10) = (1)/(-10) or v_(2) = infty`
The virtual image is formed at an infinite distance to the left of the second lens. This acts as an object for the third lens.
`(1)/(v_(3)) - (1)/(u_(3)) = (1)/(f_(3)) " " or " " (1)/(v_(3)) = (1)/(infty) + (1)/(30) " or " v_(3) = 30` cm
The final image is formed 30 cm to the right of the third lens.