The Impact of Tube Length and Magnification on Objective Focal Length

Introduction

In optical systems, particularly in microscopy and macro photography, the relationship between magnification, focal length, and tube length is a critical consideration. However, a common misconception exists about the direct influence of these factors on the focal length itself. This article explores the correct relationships and provides a detailed analysis based on fundamental optical principles.

Understanding Focal Length

The focal length of a lens is a fixed characteristic that represents the distance from the lens to the point where light rays converge or are focused. It is constant and unaltered by changes in tube length or magnification, unless one is dealing with a zoom lens. For fixed focal length lenses, which are the focus of this discussion, altering the tube length or magnification does not inherently change the focal length.

Effect of Tube Length on Magnification

The relationship between tube length, magnification, and focal length can be understood through the following optical formulae:

Focal Length Formula (reduced form): 1/u 1/v 1/f

Magnification Formula 1: m v / u

Magnification Formula 2: m (v - f) / f

Here, u represents the distance to the subject, v represents the distance to the image plane (the tube length), and f represents the focal length. The first formula indicates that as the distance to the image plane (v) increases, the distance to the subject (u) decreases. When you extend the lens from the image plane, you can focus on subjects that are closer.

The second formula, m (v - f) / f, directly relates the magnification to the subject and image distances. It shows that magnification is the ratio of the subject distance to the image distance.

Direct Relationship Between Magnification and Tube Length

Given the two formulae, we can derive a more direct relationship for magnification through the third formula:

Magnification (v - f) / f

This formula reveals that magnification is directly proportional to the additional tube length (v) beyond the focal length (f). For example, if you have a 50 mm lens with a focal length of 50 mm, and you extend the tube length by another 50 mm, the magnification will be:

Magnification (100 mm - 50 mm) / 50 mm 1

Additionally, the aperture of the lens will double, reducing it to f/8 from f/4, although this is not part of the original question but is a valuable insight to consider in macro photography.

Real Aperture and Macro Photography

Another important consideration in macro photography is the real aperture, which is often misunderstood. The aperture is written as f/8, where 8 is a fraction of the focal length. However, for optical purposes, it is more accurate to consider the aperture as a fraction of the image distance (v) rather than the focal length (f).

When distances are normal, v is approximately equal to f, making the relationship f/8 useful. However, as the distance to the image plane (v) becomes much larger, the relative aperture decreases. This effect must be compensated for in macro photography to maintain proper exposure and depth of field.

In conclusion, while focal length remains constant, the relationship between magnification, tube length, and subject distance is key to mastering optical systems in fields like microscopy and macro photography. A clear understanding of these relationships can lead to improved imaging results and more efficient lens usage.