A camera has a telephoto lens of 240-mm focal length. The lens can be moved in and out a distanc

step 1 We have object distance equals 1 over f minus 1 over q inverse of that. The focal length is give

A camera has a telephoto lens of 240-mm focal length. The...

A camera has a telephoto lens of $240-\mathrm{mm}$ focal length. The lens can be moved in and out a distance of $16 \mathrm{~mm}$ from the film plane by rotating the lens barrel. If the lens can focus objects at infinity, what is the closest object distance that can be focused?

Key Concepts

Image Distance Adjustment

In many optical systems, especially cameras, the lens is deliberately moved relative to the film or sensor to adjust the image distance. This adjustment allows the system to focus on objects at various distances by compensating for the changes in the object-to-lens distance.

Thin Lens Equation

This fundamental equation in optics relates the focal length of a lens to the distances of the object and its image from the lens (1/f = 1/do + 1/di). It is essential for understanding how adjustments in the position of a lens affect the focus, particularly the image distance needed to form a sharp image of an object at a given distance.

Focal Length

The focal length of a lens is a measure of its optical power, defined as the distance over which initially parallel rays of light are brought to a focus. It is central to determining the convergence of light and is critical in assessing how the lens performs under different focusing conditions.

Object and Image Distance Relationship

Understanding the interplay between the object distance (distance from the lens to the subject) and the image distance (distance from the lens to the sensor or film) is crucial in optical design. This relationship, governed by the thin lens equation, describes how focusing adjustments are made to create a clear image by aligning the image plane with the lens’s focal point.

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