Figure 36.36 diagrams a cross section of a camera. It has a...

Figure 36.36 diagrams a cross section of a camera. It has a single lens of focal length $65.0 \mathrm{mm},$ which is to form an image on the film at the back of the camera. Suppose the position of the lens has been adjusted to focus the image of a distant object. How far and in what direction must the lens be moved to form a sharp image of an object that is 2.00 $\mathrm{m}$ away?

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Key Concepts

Focus Adjustment

In many optical systems, such as a camera, the lens must be moved relative to a fixed image plane (film) to adjust for different object distances. When an object moves closer than infinity, the image distance increases beyond the focal length, necessitating a corresponding shift in the lens position to keep the image in focus.

Image and Object Distances

These distances quantify the positions of the object and its image relative to the lens. The object distance (do) is the distance from the lens to the object, while the image distance (di) is the distance from the lens to the plane where the image is sharply formed. Accurate knowledge of these distances is crucial for focusing.

Thin-lens Equation

This equation, given by 1/do + 1/di = 1/f, is central to understanding image formation in optics. It relates the object distance (do), image distance (di), and the focal length (f) of a thin lens, allowing one to determine the location of the image for a given object distance and lens focal length.

Focal Length

The focal length of a lens is the distance over which initially collimated rays are brought to a focus. It is a fundamental property that determines the lens's converging or diverging power and indicates where a sharp image of an object at infinity will be formed.

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