Consider these two questions: 1. I have a +40cm focal length convex lens. If I w

Question

Consider these two questions:

1. I have a +40cm focal length convex lens. If I want to produce an image of the bulb that is enlarged by a factor of 2.00, how far from the wall should the lens be placed?

The answer is 1.2m, which is acquired by:

m = -di/do, expressing di in terms of do, and plugging into the standard lens equation to find the answer.

Here, the image is real (because it converges to a wall), and it is enlarged, so it must be inverted. It therefore makes sense that m should be -2 instead of 2. Using this does give me my answer.

However, consider the second question.

2. A small insect viewed through a convex lens is 1.4cm from the lens and appears twice its size. What is the focal length of the lens?

Applying the same technique to the first, i replaced m with -2, yet I got the wrong answer. It should be calculated using +2.

Could somebody explain to me the basis behind this difference? Even though both are convex lenses and produce real images. Will rate lifesaver for a good explanation. No calculations needed (I know all of them anyway).

Explanation / Answer

Object distance is do = 1.4 cm magnification m = 2 By the defination of magnification                m = - di/do                2 = - di/do then image distance                 do = - 2 (di)                      = - 2(1.4 cm) = -2.8 cm ----------------------------------------------------------------------- From lens formula           1/f = 1/di + 1/do Therefore the focal length is              f = di do / di +do                = (1.4 cm) (-2.8 cm ) / -2.8 cm + 1.4 cm                = 2.8 cm ----------------------------------------------------------------------- ----------------------------------------------------------------------- Given tha it appears twice its size means m = 2 only not -2 Here -2 represents inverted image. So when it twice means we should take only m = 2

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