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In the last video, I showed
that a bunch of triangles

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are similar to each
other to come up

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with the relationship
between the focal length,

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the distance of an object
from the convex lens,

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and the distance of the image
of an object from that convex

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lens.

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And I realized that there was
one extra low-hanging fruit

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based on all of the
geometry that I had done,

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another relationship that
might come in useful.

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And that's the relationship
between the size

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of the object-- or maybe
since it's an arrow here,

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we can call it the
height of the object,

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and the height of the image.

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And we really set up
everything already.

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We already figured out that
this triangle over here

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is similar to this
triangle down here.

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And we figured out
in the last video

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that this triangle over here
is similar to this triangle

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over here.

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And since these
two are similar, we

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could say that A is to
B-- we did this over here.

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I'll rewrite it.

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A is to B as-- and both
of those are the sides

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opposite the right angles of
these two similar triangles.

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So that's going to be the same
thing as the ratio of the sides

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opposite this yellow
angle right over here.

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So in this triangle over here,
since we started with A first,

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it's this height
right over here.

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Now what is this
height right over here?

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This is the height
of the object.

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So this is the
height of the object

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is to-- Now what is
this opposite side

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of this yellow angle
right over here?

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Well, this is the
height of the image.

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Or we know from the
last video the distance

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of the object to the
distance of the image

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is the same thing as A to B.

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So this is going to be
the same thing as this.

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So the ratio of the
distances is also

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the same thing as the
ratio of their heights.

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So let me write it this way.

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So the ratio of the distance
from the object to the lens,

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to the distance from
the image to the lens,

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is the same as the
ratio of the height

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of the object to the
height of an image,

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or to the image of that object.

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So I just wanted to do that
little low-hanging fruit there,

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since we set up all of
the mechanics already.

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Anyway, hopefully you
found that useful.