Object Image Height and Distance Relationship
⇐ Use this menu to view and help create subtitles for this video in many different languages. You'll probably want to hide YouTube's captions if using these subtitles.
- 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 lens,
- and the distance of the image of an object from that convex lens.
- And I realize that there is 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 objects.
- maybe we set the arrow here, we call it the height of the object
- And the height of the image
- We did, we really setup everything already.
- We already figure out, that this triangle over here,
- is similar to this triangle down here
- And we figured out the in last video, that this triangle over here is similar to this triangle over here
- And since these two are similar, we can say that A is to B
- We did this over here, I will rewrite it
- A is to B as
- Both of those are the sides opposite the right angles of these 2 simlar triangles,
- So that's going to be the same thing as the ratio of the sides
- opposite this yellow angle right over here.
- so, this triangle over here, since we started with A first,
- is this height, right over here.
- Now, what is this height right over here?
- This is the height of the object.
- Is to
- Now, what is this opposite side of this yellow angle right over here
- This is the height of the image.
- Or, we know 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
- The ratio of the distance from the object to the lens
- to the distance from the image to the lens is the same
- as the ratio of the height of the object to the height of the image
- or, to the image of that object
- So I just want to do the low hanging fruit here
- since we had already done all of the...
- We had setup all of the mechanics already.
- Anyway, hope you found this useful.