Geometrical optics. Photometry. Quantum nature of light > Optical systems > Problem 13.3.20

Statement

The system consists of two identical lenses with a common optical axis. Distance between lenses , focal length of lenses . Find the focal length of the system if .

Solution

Suppose a light source is placed at the focal point of the optical system at , which is at the distance from the left lens. The (virtual) image produced by the left lens must be at the focal point of the right lens at in order for parallel light rays to emerge from the right lens. Thus,

Consequently,

Therefore, the focal length of the system is .

Answer