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

The image is virtual. Distance is greater than f.

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

Hey, guys. I hope you're able to do this problem on your own. If not, here's a little bit of help. If an object is placed within the focus of a converging lens, meaning it's at a distance less than the focal length, will a real image form? If so, does it form at a distance less than or greater than the focal length? Okay. This doesn't come with an image so we're gonna have to draw something that represents the lens and the object. Okay? So I'm just gonna draw a flat line that represents our central axis and I'm just going to draw a vertical line that represents our lens. Okay? I don't actually need to draw what the lens looks like because it's irrelevant. I know it's a converging lens. I know the rules that apply to it and all we care about are the lines of going to the center line of the lens anyway. Okay? So I'm gonna mark some distance. I have to just I have to choose how I'm gonna gonna do this because I want it to be somewhat right. Here will be one focus. Okay? Here will be the other focus. Alright. And that's as good as it's gonna get with my protractor that doesn't have a ruler on it. Alright? But that is life. Okay? And here's my object within the focus of this lens. Okay? So I'm just gonna draw my rays like I normally would. Here's one that starts central sorry. A lot parallel to the central axis, then it goes through the focus. Okay? Next, I'm just gonna draw one that goes straight through the center of the lens undeflected. The reason is is that I can't I clearly can't draw a line through the near focus because the near focus is behind my object. So my only other choice is to draw our 3rd type of ray which goes like this. Now in this image it's pretty clear to see that these are divergent lines. These are lines that are pointing away from one another so there's no real image that's going to be formed. However, ray diagrams are really tricky I'm gonna do so by looking at 2 triangles. This red triangle right here and this blue triangle right here. Okay? So the blue triangle has a base of the focal length. Right? It goes from the center line of the lens to the focus and it has a height of the object, and this is some angle phi. The red triangle also has the height of the object, but it has a length l less than the focal length and so there's some angle phi right here and it's clear because the red triangle is shorter than the blue triangle that that angle, sorry this one should be theta not phi, we can't call them both phi, it's clear that the blue triangle with the longer base has a larger angle That phi is greater than theta. Okay? So the blue line is moving away from the red line. Okay? If the red ray had a larger angle than the blue one, they would be moving together. Okay? So this is an instance where we have no real image being formed, but we do have a virtual image being formed actually. If I extend these rays backwards to see where they appeared to come from, right, they didn't actually come from here, but they appear to our eyes to have come from back here, and I extend the red one, We can see an apparent convergence, That means that there's a virtual image and it's obviously upright. Now in this diagram it appears to be located at the focus but I wouldn't trust that because these diagrams are notoriously difficult to draw especially if I have no way of properly measuring the focuses, properly measuring angles, etcetera. But this situation will most definitely produce a virtual image that is most definitely upright as it should be because all virtual images are upright. Alright, guys. That wraps up this problem. Thanks for watching.

Struggling with Physics with Algebra?

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

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