A 2.1-cm-diameter spider is 2.47 m from a wall. Determine the focal length of a

Question

A 2.1-cm-diameter spider is 2.47 m from a wall. Determine the focal length of a lens that will make a half-size image of the spider on the wall.Determine the position (measured from the wall) of a lens that will make a half-size image of the spider on the wall. Please explain solution step by step and with picture, if possible. Trying to understand the concept. THANKS

Explanation / Answer

1/f = 1/si + 1/so where so is the distance from the lens to the object and si is the distance from the lens to the image. You want to project a real image, so the image height hi and the object height ho will have different signs. You want the image height hi to be 1/2 the object height ho, so hi / ho = -1/2 = - si/so --> 2 si = so si + so = 2 m --> si + 2si = 2m --> si = 2/3 m, so = 2(2/3 m) = 4/3 m --> 1/f = 1/(2/3m) + 1/(4/3m) = 3/2m + 3/4m = 9/4m --> f = 4/9 m

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