An image is located at 4f, where f is the focal length, after it exits the lens. What is the object distance in terms of the focal length?

p = 4/3   f

Explanation:

The constructor station describes the position of the image object in relation to the focal length

         1 / f = 1 / p + 1 / q

where f is the focal length, p and q are the distances to the object and the image respectively

 the objent distance  is

         1 / p = 1 / f - 1 / q

they indicate that the image is located at q = 4f this distance is positive because the image is after the lens

        1 / p = 1 / f - 1 / 4f

        1 / p = 3 / 4f

         p = 4f / 3

the object is positive because it is to the left of the lens, according to the optical sign convention

The sign convention is that the distance to the objects is positive if it is on the left side of the lens and the image is positive if it is on the right side of the lens.

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