A 14-mm tall postage stamp is 4.0 mm from a converging lens.If the image of the stamp is 4.0 mm tall,how far is it from the lens?

Question

Quizplus · Accepted Answer

Given that the image height and object height are the same, the magnification (m) is 1 (since m = image height / object height = 4.0 mm / 4.0 mm = 1). For a converging lens, magnification is also given by m = - image distance (v) / object distance (u). Since m = 1, we have 1 = -v / u. Given that the object distance (u) is 4.0 mm, we can rearrange the equation to solve for v, the image distance. Plugging in the values, we get 1 = -v / -4.0 mm, which simplifies to v = 4.0 mm. However, this direct approach overlooks the correct method for solving the problem, which involves the lens equation 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance. Without the focal length, we cannot directly solve for v using the information provided. The correct approach involves recognizing the error in the initial reasoning and understanding that additional information or a different method is needed to find the correct answer. My initial explanation led to an incorrect conclusion based on the magnification formula, not properly accounting for the lens equation's requirements. The correct answer should involve correctly applying the lens equation and magnification formula, but without the focal length or additional details, the solution provided was incorrect.

A 14-Mm Tall Postage Stamp Is 4