Question: An object is located to the left of a convex lens whose focal length i

Question

Question: An object is located to the left of a convex lens whose focal length is 36cm. the magnification produced by the lens is m=3.0. a. To increase the mag to 4.0, should the object be moved closer or farther?Explain b. calculate the distance through which the object should be moved....

I think the answer in the book is difficult. since 3 is given as positive then the value for image distance must be negative since m=-d(image)/d(object), so then the object distance must be between the focal point and the lens---- is this logical reasoning?

Explanation / Answer

Let u & v be the distances of object and image from the lens. Formula for Magnification, m=v/u Let the initial distances (for m=3) be u1 & v1, and final distances (for m=4) be u2 & v2. Then, v1=3u1 and v2=4u2 Put these relations into the lens equation one by one to get the values of u1 and u2, 1/f= 1/v - 1/u For f=36 cm and v1=3u1, you'll get u1=-24cm, and for v2=4u2, you'll get u2=-27cm =>the object has to be shifted away from the lens (in order to get m=4), by a distance of 3 cm. please rate.

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