To focus a camera on objects at different distances, the...

To focus a camera on objects at different distances, the converging lens is moved toward or away from the image sensor, so a sharp image always falls on the sensor. A camera with a telephoto lens $(f=200.0 \mathrm{mm})$ is to be focused on an object located first at a distance of 3.5 $\mathrm{m}$ and then at 50.0 $\mathrm{m}$ . Over what distance must the lens be movable?

Key Concepts

Image Distance Adjustment

The change in image distance with object distance is a key concept in optical imaging. For objects at different distances, the point at which the image is in focus shifts, and the sensor or lens must be moved accordingly to compensate for this shift. This adjustment is critical for achieving clear images regardless of the subject's distance.

Lens Movability

Lens movability refers to the range over which the lens must be adjusted to account for changes in object distance. By calculating the difference between the image distances corresponding to the closest and farthest objects in focus, one can determine the necessary movement range of the lens, highlighting an essential aspect of the design in camera focusing mechanisms.

Thin Lens Equation

The thin lens equation, given by 1/f = 1/d? + 1/d?, is a fundamental relation in geometrical optics that connects the focal length of a lens (f) with the object distance (d?) and the image distance (d?). This equation is used to determine where an image is formed relative to the lens and underpins the principles of image formation in cameras and other optical systems.

Focusing Mechanism

Focusing in optical devices involves adjusting the relative positions of the lens and the image sensor so that the image is formed precisely on the sensor. This is necessary because the ideal image distance changes when the object distance changes, requiring mechanical or optical adjustments to maintain image sharpness.

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