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Current time:0:00Total duration:2:22

Object image height and distance relationship

Video transcript

in the last video I showed that a bunch of triangles are similar to each other to come up with a relationship between the focal length the distance of an object from the convex lenss and the distance of the image of an object from that convex lens and I realized that there was one extra low-hanging fruit based on all of the geometry that I had done another relationship that might come in useful and that's the relationship between the size of the object or maybe we since it's an arrow here we call it the height of the object and the height of the image and the height of the image and we did we really set up everything already we already figured out that this triangle over here this triangle over here is similar to this triangle down here and we figured out in the last video that this triangle over here is similar to this triangle over here and since these two are similar we could say that a is to V we did this over here I'll rewrite it a is to B as a and both of those are the the sides opposite the right angles of these two similar triangles so that's going to be the same thing as the ratio of the sides opposite this yellow angle opposite this yellow angle right over here so in this triangle over here since we started with a first it's this height right over here now what is this height right over here this is the height of the object this is the height of the object so this is the height of the object is 2 now what is this opposite side of this yellow angle right over here well this is the height of the image height of the image or we know that from the last video the distance of the object to the distance of the image is the same thing as a to B so this is going to be the same thing as this so the ratio of the distances is also the same thing as the ratio of their heights so let me write it this way so the ratio of the distance from the object to the lens to the distance of the from the image to the lens is the same as the ratio of the height of the object to the height of an image or to the image of that object so I just wanted to do that little low-hanging there since we had already done all of all of the we've set up all of the mechanics already anyway hopefully you found that useful