Two converging lenses having focal lengths of f 1 = 10.5 cm and f 2 = 20.0 cm ar

Question

Two converging lenses having focal lengths of f1 = 10.5 cm and f2 = 20.0 cm are placed d = 50.0 cm apart, as shown in the figure below. The final image is to be located between the lenses, at the position x = 32.3 cm indicated.

a) How far to the left of the first lens should the object be positioned?

b) What is the overall magnification of the system?

Explanation / Answer

Suppose image formed by f1 is v1 to its right. So, for first lens 1/v1 - 1/f1 = 1/u1 So, 1/v1 - 1/10.5 = 1/(-p) Also, for second lens, 1/v2 - 1/f2 = 1/u2 1/(-d + x) - 1/f2 = 1/(-d + v1) So, 1/(-50 + 32.5) - 1/20 = 1/(-50 + v1) So, 1/v1 = 1/10.5 - 1/p and -1/17.5 - 1/20 = 1/(v1 - 50) => -0.10714 = 1/(v1 - 50) So, 9.333 = 50 - v1 So, v1 = 40.67 cm So, 1/40.67 = 1/10.5 - 1/p So, p = 14.15 cm So, image is to be placed 14.5 cm to the left of the first lens. Now, magnification = m1*m2 = (v1/u1)*(v2/u2) = (-40.666/14.15)*(-50 + 32.5)/(-50 + 40.666) = +5.39

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