An object is located to the left of a convex lens whose...

An object is located to the left of a convex lens whose focal length is $34 \mathrm{cm}$. The magnification produced by the lens is $m=3.0 .$ (a) To increase the magnification to $4.0,$ should the object be moved closer to the lens or farther away? Explain. (b) Calculate the distance through which the object should be moved.

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Key Concepts

Thin Lens Formula

This concept involves the fundamental relationship for lenses given by 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. It is crucial in understanding how the positions of the object and image are interrelated for any lens, particularly a convex (converging) lens, and it allows for the calculation of unknown distances when one is provided.

Magnification in Lens Systems

Magnification in lenses is defined as the ratio of the image height to the object height and is given by m = -di/do, where the negative sign indicates image inversion in the case of real images. This concept is key to understanding how changes in the object distance affect the size of the image, as an increase in magnification typically requires adjusting the object’s position relative to the lens.

Relationship Between Object Distance and Magnification

In the context of a convex lens, as the object is moved closer to the lens (but still outside the focal length), the image distance increases, which in turn typically increases the magnitude of the magnification. Understanding this relationship explains why, to achieve a higher magnification, one must often position the object closer to the lens, altering the balance established by the lens formula.

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