What determines the focal length of a lens?

I.e. what makes a 50mm lens a 50mm lens?


Quite a lot of people mistakenly believe that the focal length of a lens is the distance between the front and rear lens elements. Nope.

There is a simple answer to this question and a complex answer that involves a lot of physics and complicated formulae. Let's stick to the simple(ish) explanation.

When light passes through a lens, refraction causes the image to invert. This means that the image will appear upside down and back to front on the film (or digital sensor). In a single lens reflex camera, the image that appears in the view finder is bounced off mirrors to appear the right way up (mirrorless cameras do this electronically).

Assuming a simple, one element lens focused at infinity - the position inside the lens at which the inversion occurs is the optical center of the lens, this point is called the point of convergence. The focal length of the lens is the distance, in millimetres, from the point of convergence to the film plane.

Why this gets really complex is because lenses contain more than one element, some may include more than a dozen. As different wavelengths of light travel at different frequencies the point of convergence will be fractionally different for each wavelength. This effect is known as chromatic aberration, additional lens elements are added to correct this phenomena. Other elements and lens coatings are included for other corrections.

Regardless of how many elements are inside the lens, the calculation of the focal length is made at the equivalent distance of a single lens.

The distance from the optical center of the lens to the film plane is the focal length of the lens, measured in millimetres.

Distance from point of convergence to film plane (very inaccurate diagram)

Distance from point of convergence to film plane (very inaccurate diagram)

A more practical example

A more practical example

35mm Equivalence

I'm of the vintage that recalls 35mm as being "small format", these days it is commonly referred to as "full frame".

A 50mm lens is a 50mm lens, regardless of the camera body to which it is attached. However the size of the media recording the image, whether film size or digital sensor, will determine how much of the image is captured due to the differing angles of view.

Examples:

- a 50mm lens on a medium format camera would be considered wide angle, a normal lens on full frame, and a short-telephoto on a 4/3 system camera.

35mm equivalence is really just a convenient way of comparing different format sizes on a common basis.

Interestingly, the relationship between lens aperture and film (sensor) size is affected in a similar way. I'll write more about the affects of crop factor in another post.

A comparison of the same sized lens on different sized media

A comparison of the same sized lens on different sized media

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