A camera uses a 200.0-mm focal length telephoto lens to take...

A camera uses a $200.0-\mathrm{mm}$ focal length telephoto lens to take pictures from a distance of infinity to as close as $2.0 \mathrm{~m}$. What are the minimum and maximum distances from the lens to the film?

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Key Concepts

Image Distance

Image distance refers to the separation between the lens and the image plane (or film) where the image is in sharp focus. Its value changes with the distance of the object being imaged, and it is calculated using the thin lens equation to ensure proper focus across different object distances.

Focusing Mechanism

A focusing mechanism adjusts the position of the image plane relative to the lens to achieve sharp focus for objects at varying distances. This adjustment is essential in photography and other imaging systems to accommodate subjects from infinity down to a close minimum distance.

Thin Lens Equation

This is a fundamental relation in geometric optics that links the focal length of a lens to the distances of the object and the image (or film) from the lens. It is expressed as 1/f = 1/d_o + 1/d_i and is crucial for determining where an image forms relative to the lens for objects at various distances.

Focal Length

The focal length is the distance from the lens at which parallel rays of light converge to a point. It determines the magnification and field of view of the lens, with longer focal lengths providing higher magnification and narrower fields of view, and is a critical parameter in lens design and function.

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