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

Explanation

Image formed by the first lens

`(1)/(v_(1))-(1)/(u_(1))=(1)/(f_(1))`
`(1)/(v_(1))-(1)/(-30)=(1)/(10)`
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)=oo`
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)/(oo)+(1)/(30)`
`or v_(3)=30cm`
The final image is formed 30 cm to the right of the third lens.