Prove a lens must always be converging if

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    Converging Lens
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A lens must be converging to produce an upright, enlarged image, as concave lenses only create virtual, reduced images. The discussion emphasizes the need for mathematical proof, suggesting that ray diagrams can visually demonstrate this principle. Converging lenses, such as convex lenses, are the only type capable of enlarging images while maintaining an upright orientation. Understanding the properties of lens types is crucial for solving this problem. Therefore, a converging lens is essential for achieving the desired image characteristics.
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Prove a lens must always be converging if...

Consider a single lens with the object on the left side. Prove that for an upright, enlarged image that the lens must always be converging. I'm assuming my professor wants this to be mathematically proven, but I have no idea how to do so...HELP! I don't even know where to begin with this question
 
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Well, conceptually, a concave lens will ALWAYS produce an image that is virtual and reduced in size. So, if you want an enlarged image, your lens NEEDS to be converging - there are no other options.

You could prove this by drawing lens ray diagrams. If you haven't learned how to draw those, they're pretty simple! Here's something that might be helpful :
http://www.physicsclassroom.com/class/refrn/u14l5da.cfm
 

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