2. A camera has a single converging lens with a fixed focal...

2. A camera has a single converging lens with a fixed focal length f. (a) How far should the lens be from the film in order to focus an object that is infinitely far away (namely the incoming light rays are parallel with the principal axis of the system). (b) How far should the lens be from the film to focus an object at a distance of 2f in front of the lens? (c) What is the magnification of the image in part (b)? (d) Is the image in part (b) real or virtual? (e) Is the image in part (b) inverted? (f) If the camera can focus on objects at infinity and the lens can only move a distance f/2, what is the minimum distance at which an object can be focused? aperture ring shutter speed control lens shutter diaphragm focusing ring film

Transcript

00:01 So here we're going to start with the imaging formula for a thin lens.

00:06 So it's called the thin lens equation.

00:10 And we'll just talk about that a little bit.

00:13 And then take a look at an example of where this may be applied with a camera lens.

00:20 So that there is a lens, a single lens, and there is an object somewhere near the lens.

00:31 The lens usually has a focal point.

00:35 That is positive.

00:38 And actually there are two focal points, but the focal length is positive.

00:43 The focal point on the outgoing side of the lens is usually called the primary, f and f prime on the incoming side is called the secondary.

00:57 But we measure distances from the lens, so the object has an object distance that we call s, and the image forms somewhere, depending on where the object is, we'll call that s prime.

01:13 And this is just a sketch, but f is the focal length taken to be a positive quantity for a converging lens, which is what a camera is.

01:29 So we'll start with that.

01:31 S is the distance the object is from the lens, and s prime is the image distance.

01:51 And i'll just kind of sketch an image in there.

02:06 So the thin lens equation assumes that the lens is thin in profile, compared to the distance is involved.

02:16 And it's a very simple formula.

02:19 1 over s plus 1 over s prime is equal to 1 over 3.

02:23 F.

02:25 So that's the thin lens equation.

02:27 There is a secondary equation for the magnification of the image, and it is minus s prime over s.

02:42 So yeah, you can get different magnifications.

02:46 So let's take a look at an example with the lens in a camera.

02:50 So typically a lens is actually made of multiple lenses that exist, in a barrel.

03:01 And we won't get into that.

03:02 We're going to treat that whole barrel as if it acts like a single lens.

03:08 And those multiple lenses allow some zooming.

03:13 They allow some chromatic admiration corrections, et cetera.

03:21 But your box of your camera has the imager in it.

03:26 Most people don't use film nowadays.

03:28 They use a digital ccd camera, but we won't get into that.

03:35 The barrel itself usually allows you to move the lenses back and forth with a moving ring.

03:46 And that is going to allow you to focus on different object distances.

03:52 That's an important concept that object distances, according to this formula, will need to have a different image distance, so you're going to have to fix that distance between the lens and your imaging device inside the camera box.

04:13 Okay, so let's take a look at an example.

04:17 Where does an image form with object and infinity? and we won't say infinity, we'll just say very far away.

04:37 So let's say you're looking at taking a picture of some faraway mountains...

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