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## Pixar in a Box

### Course: Pixar in a Box > Unit 6

Lesson 2: Mathematics of depth of field# Out of focus objects

In this video we'll explore what happens when an object is out of focus from a geometric perspective.

## Want to join the conversation?

- At1:59, is that the radius of the blur, or the diameter?(6 votes)
- It is actually the radius of the circle of confusion and not the diameter. It is easy to be confused, because I think the sketch is a bit misleading. It depicts only half of the ray bundle that is emitted from point P, namely the bundle between points D and E. One should imagine another point, let's call if F, symmetrical to point D with point E as the center of symmetry. Now, imagine the rest of the rays that originate from point P and pass through the lens with outermost the ray passing through F. These rays obviously also converge on point A by the bending of the lens. Then, if you extrude this outermost ray to meet the image plane, you will have the full diameter of the circle. I understand, it sounds much more complicated in writing than in sketches, but hopefully, it helped.(6 votes)

- He talks about "moving the Image Plane". I forgot - what exactly determines the distance from the pinhole to the image plane? Because in one video I thought he said the Image Plane was positioned at the focal point. What did I miss? Because that is obviously wrong.

A quick explanation is all I need, thanks!

I have been watching these videos in a*blur*of*confusion*, I'm seeing*circles*all around me. :\

In all seriousness, I really enjoyed all these videos! :-)(2 votes) - What would the out of focus do?(1 vote)
- I am so lost thaat i do not now what to do(1 vote)
- At1:59, is that the radius of the blur, or the diameter?(1 vote)
- I'm confused. I believe I understand what he is saying in the video, but having trouble picturing this in a real camera. I assume the focal point is fixed for a given lens. Does the image plane move? Is that how you can get a lens with a range of say 35mm to 70mm? Which part does the f-stop control, the aperture? And the focus control the image plane?(1 vote)
- great video! Thanks Mr VanSchieck(1 vote)
- How is BC the
**radius**of the circle of confusion, and not the diameter?(1 vote) - At1:59, is that the radius of the blur, or the diameter?(1 vote)
- It is the radius of the blur, not the diameter(0 votes)

- Which film is the shot with the caterpillar from?(0 votes)
- It is from Toy Story. Right after this shot, Buzz Lightyear pushes away the leaf to walk through the bushes.(3 votes)

## Video transcript

- Welcome back. Now that you're getting comfortable with the simple lens law,
let's go a little deeper. In the previous exercise you
found that the simple lens law can be written as i equals o
times f, divided by o minus f. So if the image plane in
our camera is at distance i, objects at distance o from the camera will come into crisp focus. But what about objects
at some other distance? Well, they'll be blurry. They're not in crisp focus. For example, the in-focus
leaves are at a distance that satisfies the simple lens equation. However, the objects in the
background are blurred out. And notice how the blur is
in the shape of a circle. Recall from the last lesson, we called this a circle of confusion. But how big is the circle? To answer that question,
in the rest of this lesson we'll develop a formula that describes the size of the circle, given
things like the focal length of the lens, the aperture, and
the distance to the object. As before, let's look
at this problem in 2-D and consider what happens to a point P with coordinates x zero, y zero, at a distance o from the lens. We can intersect the
parallel and medial rays to find the point where
P comes into focus. Let's call this A. And remember, every lens has an aperture, which restricts which rays
make it into the camera. Let's put a point E at
the center of our lens and a point D at the top of the aperture. In other words, DE is the
radius of our aperture. So all light rays from
P which pass through DE end up focusing at the same point A. And if the image plane
is at this distance i, then P will be in sharp focus. But if the image plane is at
a larger distance, i prime, say over here, then P's
image gets blurred out, into the region denoted BC in the diagram. This distance BC defines the size of the circle of confusion, that is, BC is the radius of the blur. Okay, let's pause here so
you can get comfortable with this diagram before
we finish our calculation.