# Two lens system – Image distance and magnification

Two converging lenses, with the focal length f1 = 10 cm and f2 = 15 cm are placed 40 cm apart, as shown on the figure. An object is placed 60 cm in front of the first lens as show in second figure.
a) Find the position of the final image formed by the combination of the two lenses?
b) Find magnification of the final image formed by the combination of the two lenses? L - Distance between two lenses f1 - Focal length of first lens f2 - Focal length of second lens do1 - Distance to object di1 - Distance to image created from first lens do2 - Distance to object for second lens (which is the image create from first lens) hi1 - First image height hi2 -Second image height m1 - magnification for first lens m2 - magnification for second image To determine the image distance, the lens equation can be used. Apply lens equation to first lens    di1 = 12 cm First image located 12 cm behind the first lens Image generated from first lens going to be object for the second lens do2 = L – di1 do2 = 40 cm – 12 cm do2 = 28 cm Lets apply lens equation to second lens   di2 = 32.31 cm Final image located at 32.31 cm behind second lens. Lens magnification can be find using  m1 = - 0.2 First lens has magnification of – 0.2 Image magnification in terms of object and image height can be write   First lens has magnification of – 0.2, the image is inverted and is 0.2 times of original height. Lets apply image magnification equation to second lens  m2 = - 1.15 Second lens has magnification of – 1.15 Image magnification in terms of object/image height is  Image generated from first lens going to be object for the second lens hi1 = ho2     From this equation we see that total magnification is the product of m1 and m2. Total magnification is 0.23, is a positive number, final image is not inverted but it is smaller than original object.