An object is placed 36cm36\operatorname{\mathrm{cm}} to the left of a convex lens, an image is formed 20cm20\operatorname{\mathrm{cm}}20cm to the right of the lens. What is the focal length of this lens?

12.86cm⁡12.86\operatorname{\mathrm{cm}}

An object is placed 36 c m 36\operatorname{\mathrm{cm}} to the left of a convex lens, an image is formed 20 c m 20\operatorname{\mathrm{cm}} 20 cm to the right of the lens. What is the focal length of this lens?

All right folks, so let's get a bit more practice with convex lenses. So, in this practice problem, we have an object that's placed 36 centimeters to the left of the convex lens, and then we have an image that's formed at 20 centimeters to the right of the lens. All right. We're supposed to use this to figure out what is the focal length of this lens. So remember that's just the variable little F. Now, before you start plugging in these equations. And messing around with all the numbers. Again, just try to draw the diagram. It's gonna be really, really helpful here. It's gonna be really good practice, and you'll often need it for your problems. So, I'm just gonna keep extending this sort of forward like this. It doesn't have to be perfect, it's just a sketch. So, we've got a convex lens, Remember that's one that bulges out like this, and I've got an object that is placed over here. So this is gonna be my object. And then, remember, what happens here is we have an object that's to the left of the lens, and we have an image that forms to the right. So, whenever we have an image that forms in the opposite of the side of the lens, it's gonna be uh it's gonna be upside down and it's also gonna be a real image. If you put a screen there, you would actually see it. And again, just try to get some practice drawing your array diagram. So, if you draw your Pray that goes parallels first, and then it sort of bends down towards the focal length, if you don't exactly know where the focal point is, just sort of like estimate. Made it. You've got the F-ray that's gonna go sort of through the near F, and then it's gonna straighten out, and then you're eventually gonna have an image that forms over here somewhere. So again, it doesn't have to be perfect, and again, it might not be to size to scale and whatnot, but this is gonna be where the image forms. The rays converge underneath the axis, so it's gonna be upside down, and it's gonna be uh sort of somewhere over here. This is gonna be my image. All right, so let's use this now to figure out what our focal length is. So we're basically just trying to figure out what's the focal length of the lens. So now we can go ahead and start using our equations here. We have 1 over D plus 1 over DI is equal to 1 over F. Remember, we use the same exact equation here that we did for mirrors. So if I'm looking for the focal length, I just need to plug in my DO and my DI. Remember, worry about plugging in the numbers first and then we'll attach signs to them. So, for example, do we know our DO? That's just the object distance, which is 36 centimeters to the left of the lens. Towards this distance over here is 36, but is it positive or negative? Let's check the rules. The rules say for lenses that it's basically just the same thing as a, uh, like we like we did for mirrors, where it's gonna be positive if the image or the object is on the same side as the inbound rays. Inbound rays are basically just what happens before it hits the mirror or lens. So these are going to be my inbound rays, right? So, these are my, let's do this in black. So these are my inbound. Rays. So, the object is on the same side as those inbound rays, therefore, this is going to be positive. So, this is gonna be 1/36 plus. And then what about DI? My DI is gonna be the images formed 20 centimeters to the right of the lens. Again, it doesn't have to be perfect here, but this distance over here is going to be my DI and we know this is equal to 20, all right? So, is this a positive or a negative number? We have an image that forms on the same side as the outbound rays. So, these are my outbound rays. So this is what happens after it goes through the lens, and the DI is positive if the image is on the same side. So, this DI is also going to be positive. So, I'm just going to do 1/36 plus 1/20 is equal to 1 over F. So again, if you just put these in parentheses and then add those fractions, you should get. A decimal when you plug this into your calculators, but you should get something like 0.07 is equal to 1 over F. All right? So now all we do is we basically just uh take the reciprocal, never forget you're supposed to take the reciprocal of that last, uh, decimal that you get. A lot of times students have a habit of just writing that number, but you have to take the reciprocal, all right? So this is gonna be your focal length, and this is gonna be about 12.86. All right? Now again, this is the variable that we were trying to find. So we don't plug in any signs for this. Always use the signs for your known quantities and then you'll determine and then once you figure out the sign of your unknown, your target variable, you can kind of make sense of it, right? So we got a positive number which is a positive focal length, and that makes sense because remember, the rule is that you have F is positive for convex lenses and negative for concave, all right? The fact that we get a positive number totally makes sense there, all right? So that's it for this one. Let me know if you have any questions and I'll see you, I'll see you in the next one.

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An object is placed 36cm36\(\operatorname{\mathrm{cm}\)} to the left of a convex lens, an image is formed 20cm20\(\operatorname{\mathrm{cm}\)}20cm to the right of the lens. What is the focal length of this lens?

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An object is placed $36 c m$ to the left of a convex lens, an image is formed $20\(\operatorname{\mathrm{cm}\)}$ to the right of the lens. What is the focal length of this lens?