#1: By holding a magnifying glass 29cm from your desk lamp, you can focus an ima

Question

#1: By holding a magnifying glass 29cm from your desk lamp, you can focus an image of the lamp's bulb on a wall 1.8m from the lamp. What is the focal length of your magnifying glass (in cm)? For this, I understand to use lens makers law. This get the equation to be F = (u * v) / (u + v), where u = -29, v = 180, though when I plugged this in, I got, -5220 / 151 = -34.57, which was incorrect. #2: Find the focal length of a concave mirror if an object 16cm from the mirror has a virtual image 3.0 times the object's actual size. I am lost and is just unsure how to do this. Any help is greatly appreciated, will rate Lifesaver. Thanks a bunch

Explanation / Answer

You just have your signs mixed up. The image is real (because its projected on a wall), so the object and image distances, u and v, are both positive. So...

focal length = 29 * 180 / (29 + 180) =

= 25.0 cm

For the second question, object distance = 16 and image distance is negative (virtual image) and three times greater, so

image distance is -48 cm

and

focal length = 16 * -48 / (16 + -48) = 24.0 cm

You just have to watch the signs and how they relate to the definitions of real and virtual images.

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