If an object is placed within the focus of a diverging lens (it's at a distance of less than the focal length), where will the image form? If so, does it form at a distance less than or greater than the focal length?

A virtual image is formed at a distance less than f

If an object is placed within the focus of a diverging lens (it's at a distance of less than the focal length), where will the image form? If so, does it form at a distance less than or greater than the focal length?

Hey guys. I hope you were able to solve this problem on your own. If not, here's a little bit of help. If an object is placed within the focus of a diverging lens, that means it's at a distance less than the focal length, where will the image form? If so, does it form at a distance less than or greater than the focal length? Okay. So there's no image here which means that we need to draw our own. I'm gonna draw a central axis right here. Okay. I don't know why the program screwed that one up. I'm gonna draw a central axis here. There we go. And then I'm going to draw the line representing the center of my lens. I know it's a diverging lens, so I don't need to actually draw the lens. The shape of the lens is irrelevant. All I need is that central line through the middle of the lens. Okay? And now once again I need to determine where I'm going to draw my foci. I'll put one here. So, yes, that's where I wanted it, and then the other one here. Those are roughly the same distance apart. But my object is within the focus. Okay? Now the question is where is the image going to be formed, and is it going to be within the focus or outside of the Okay? Before even starting, what side of the lens do you guys think this image is gonna be formed on? The left side of the lens or the right side of the lens? It's gonna be formed on the left side. This is a diverging lens, which means light can never converge on the other side of the lens. Light can only appear to have converged on the front side of the lens. So that's where our image will be formed. So first, let's draw a line parallel to the central axis and then moving away from the focus. And then I'm gonna trace with a dashed green line where it appears to come from. Next, I'm gonna draw a line towards the far focus stopping at the center line of the lens. So towards the far focus, stopping at the center line, and then it continues parallel to the central axis. But what I'm missing is the line tracing where this appeared to come from. Okay? So right here, we have our apparent convergence of light. So that is where our image will be formed. It's going to be upright because it is above the central axis. It's going to be virtual because it's not a real convergence of light, and it's going to be to the left of the lens or in front of the lens because it's a virtual image. Furthermore, this image will always be the focal length, because this line goes straight to the focus. This line, no matter what height it intersects it at, is always gonna cross the green line within the focus. Okay? So that image distance is always going to be less than the focus. Alright guys, that wraps up this problem. Thanks for watching.

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If an object is placed within the focus of a diverging lens (it's at a distance of less than the focal length), where will the image form? If so, does it form at a distance less than or greater than the focal length?

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