A camera lens has a fixed focal length of magnitude 50.0 mm. The camera is focused on a 1.0-m -

A camera lens has a fixed focal length of magnitude 50.0...

A camera lens has a fixed focal length of magnitude $50.0 \mathrm{~mm}$. The camera is focused on a $1.0-\mathrm{m}$ -tall child who is standing $3.0 \mathrm{~m}$ from the lens. (a) Should the image formed be real or virtual? Why? (b) Is the lens converging or diverging? Why? (c) What is the distance from the lens to the film? (d) How tall is the image on the film? (e) To focus the camera, the lens is moved away from or closer to the film. What is the total distance the lens must be able to move if the camera can take clear pictures of objects at distances anywhere from $1.00 \mathrm{~m}$ to infinity?

Key Concepts

Camera Focusing Mechanism

The focusing mechanism in cameras involves adjusting the relative positions of the lens and the film (or sensor) to achieve sharp images. By moving the lens or the film, the system compensates for various object distances, ensuring that the image formed adheres to the thin lens equation and maintains clarity across a range of distances.

Magnification

Magnification is the ratio of the size of the image to the size of the object and is directly related to the distances involved in the thin lens equation. It provides insight into how the dimensions of the captured image compare to the object, which is important for understanding image resolution and scale in photographs.

Thin Lens Equation

The thin lens equation, given by 1/f = 1/d_o + 1/d_i, is fundamental in geometrical optics for relating the focal length of a lens (f), the object distance (d_o), and the image distance (d_i). This concept is key to analyzing image formation in cameras and determining the position of the film where the image is sharply projected.

Real vs. Virtual Images

This concept distinguishes two types of image formation. A real image is formed when light rays converge at a point and can be projected onto a screen, while a virtual image results from the apparent divergence of light rays, meaning the image can only be seen by looking through the lens. This understanding is crucial for interpreting how and where an image is formed in optical systems such as cameras.

Converging vs. Diverging Lenses

Understanding whether a lens is converging or diverging is essential for predicting how it manipulates light. Converging lenses (often convex) are designed to bring parallel incoming rays to a focus, forming real images under appropriate conditions. In contrast, diverging lenses (typically concave) spread out rays, generally forming virtual images. This distinction influences how lenses are applied in optical devices, including cameras.

Transcript

00:02 You're going to have a camera that is, use the pictures off this person here and for god.

00:10 A.

00:11 We use a lance in a field and we want to know in the first place if the image that is produced by this camera is spiritual or israel and france is conversion or other version.

00:25 Okay, so for cameras, the image is produced on the open side off the object because the film anything on the oh, but its eye off the object.

00:37 So in order to do that, we need a commercial where convergence, because a commercial ends produced a an image studies on the opposite side.

00:51 They burgeon alliances, only produces images.

00:55 There are all the same time of the old off the order that why we need our conversion and eso the image that is produced by your conversion and when it's produced on the opposite side is inverted and it is really and it's real.

01:14 There is no ah, another a possibility for our conversion lends to produce our virtual image, but a conversion and it's produced a co op virtual image on lee.

01:27 If this images produced on the same guy of the object and it is not a case we need that unit.

01:36 Ah, when you know the image, it will be on the opposite side.

01:42 So, uh, yeah, it's really and it's a convergent.

01:46 And in the next part of the problem, we want to compute the value off.

01:52 There is the much decent because you're remember that a we have the value of the object distance.

02:02 This is information off the problem.

02:04 And we also have focal and off the land.

02:08 Oh, in order to compute you were when i use the equation and we already have the bodies off, if anybody would be, we just need to replace the budget that we have here on earth computer cube.

02:29 So between that, we can easily see that the body who is bearable 0 51 year it and in the next part off the problem, we want to compute a the value of the final size off the image.

02:48 Well, now that we'll have q, we can use the mummification energy computer size off the final image.

02:58 It remembered.

02:59 Ah, a modification there is equal through a a prime over age.

03:09 Que is about mind cuba be oh, this from this part off the equation become completely value off a crime.

03:23 So each crime is equal minus cule dimes age over b.

03:30 And we already have all these bottles.

03:33 I'm going.

03:35 So from this a replacing the values off cue off, be in for age that the lawrences is well nearer.

03:46 We have the value off age prime in these values.

03:50 No, your boy ah, having the mirrors...