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.

Object Image Height and Distance Relationship

Object Image Height and Distance Relationship