A researcher plans to photograph a microscopic organism by using two thin lenses in sequence. Lens L1 is a converging lens with focal length 6.0 cm that produces an enlarged real image inside a transparent chamber. Lens L2 is a diverging lens with focal length −8.0 cm, placed 4.0 cm to the right of the chamber, that further adjusts the size of the image so it exactly matches the 24 mm height of a camera sensor located 12 cm to the right of L2. The organism itself is 0.60 mm tall. All components lie on the optic axis, and lens thicknesses are negligible.
(a) Determine the required overall linear magnification of the two-lens system so that the organism’s image fills the sensor height.
(b) Let so1 represent the distance from the organism to L1. Develop a set of equations that relate so1 to the intermediate image distance from L1, to the object distance for L2, and to the final sensor location.
(c) Solve the equations from part (b) to find the required value of so1 and the intermediate image distance relative to L1.
(d) Calculate the individual magnifications produced by L1 and L2 and verify that their product equals the overall magnification found in part (a). Comment on the sign of each magnification and its physical meaning in terms of image orientation.
(e) Discuss one practical limitation that may arise if so1 is positioned extremely close to the focal length of L1, making specific reference to image brightness or optical aberrations.