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

step 1 In this problem, we use a camera to take pictures of this person here. And for that, this camera

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

A camera lens has a fixed focal length of magnitude $50.0 \mathrm{mm} .$ The camera is focused on a 1.0 -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.

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.

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.

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