Two systems are formed from a converging lens and a diverging lens, as shown in

Question

Two systems are formed from a converging lens and a diverging lens, as shown in parts a and b of the drawing. (The point labeled "Fconverging" is the focal point of the converging lens.) An object is placed inside the focal point of lens 1 at a distance of 10.90 cm to the left of lens 1. The focal lengths of the converging and diverging lenses are 15.00 and ?20.0 cm respectively. The distance between the lenses is 50.0 cm. Determine the final image distance for each system, measured with respect to lens 2.

Explanation / Answer

What are the two systems? I assume that 1) the converging lens is in front, and 2) the diverging lens is in front. let s2' = distance of image from second lens s1 = distance of object from first lens (to the left, if the first lens is on the left side of the second lens) d = distance between lenses f1 = focus length of first lens f2 = focus length of second lens for the distance of the image from the second lens use 1/s2' = 1/f2 - 1/(d - f1s1/(s1 - s1)) a) converging lens is in front: 1/s2' = 1/(- 0.2) - 1/(0.5 - 0.15*0.1090/(0.1090 - 0.15)) s2' = - 0.14593 = - 14.593 cm Ans The image is 0.14593 m = 14.593 cm to the left of the second lens (in front of the second lens) b) diverging lens is in front: 1/s2' = 1/0.15 - 1/(0.5 - (-0.2*0.1090/(0.1090 - (-0.2))) ---> s2' = 0.2035 m Ans The image is 0.2035 m = 20.325cm behind the second lens

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