Question

Which of the following is the correct relation between photographic scale ($S$) and focal length ($f$) of the camera lens?

• A. $S \propto f$
• B. $S \propto (1/f)$
• C. $S \propto f^2$
• D. $S \propto (1/f^2)$

Hint:

Photographic scale $S \propto f$; longer focal length increases the scale for a given height.

Answer 1

The Correct Option is A

The photographic scale, denoted as \(S\), is a critical aspect in photogrammetry, primarily in determining the relationship between the ground objects and their photographic representations. It is defined as the ratio of a distance on the photograph to the actual distance on the ground.

The focal length (\(f\)) of the camera lens plays a significant role in determining the photographic scale. The basic equation governing the photographic scale is:

\[S = \frac{f}{H}\]

where \(H\) is the height of the camera above the ground. From this equation, it can be deduced that:

\[S \propto f\]

This means that the photographic scale is directly proportional to the focal length when the camera height remains constant. Therefore, a longer focal length results in a larger scale.

Hence, the correct relationship is \(S \propto f\).