A convex lens has a focal length . An object is placed between infinity and 2 fr

Question

A convex lens has a focal length . An object is placed between infinity and 2 from the lens along a line perpendicular to the center of the lens. The image is located at what distance from the lens?

between f and 2f <-- correct answer

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I need some help working this one out.

Lens' : 1/f = 1/d_i + 1/d_o

d_o = 1/2f

=> 1/f = 1/2f + 1/d_i

=> 1/f - 1/2f = 1/d_i

=> 2/2f - 1/2f = 1/d_i

=> 1/d_i = 1/2f

=> d_i = 2f

Assuming I did that correctly (which I may not have), why then is the correct answer between f and 2f rather than 2f?

Thanks for your assistance.

between f and 2f <-- correct answer

----------------------------------------------------------------------------------------------------------------------------

I need some help working this one out.

Lens' : 1/f = 1/d_i + 1/d_o

d_o = 1/2f

Explanation / Answer

The focal length (f) is the distance from the lens that parallel light rays entering the
lens will come together, or converge, at the same point. So an object very distant from the lens (whose light rays are essentially parallel) will produce an image at a distance f from the lens. As the object comes closer, the distance of the image will increase according to the formula: 1/do + 1/di = 1/f, where do is the distance of the object and di is the distance of the image. When the object is at a distance 2f, the image will also be at distance 2f on the other side of the lens. So when the object is between 2f and an infinite distance away, the image will be between f and 2f

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