jeweler53

Is there a simple formula for determining how far a simple lens must move to achieve a specific focus distance.

For example, A 100 mm lens must be 100 mm from the focal plane to focus at infinity. How far must the lens move to focus at 10 feet.

Thanks in advance. I have searched high and low and can't seem to find and answer. I may not be searching the correct terms though!

larryepage Loc: North Texas area

The lens formula is, in fact, very simple. It is:

(1/object distance) + (1/image distance) = (1/focal length)

There is also a corollary formula that is sometimes helpful, used to compare the image size to the object size:

Magnification = (image distance)/(object distance)

For complex systems like our camera lenses, these distances are measured from the "optical center" of the lens.

lamiaceae Loc: San Luis Obispo County, CA

You need to check those old "real" photo books. Or use Google.

photodoc16

larryepage,
How does one define 'image' distance? 'Object' distance, I assume, is the subject or point of focus of the image or photo.
Thanks,
Photodoc16

aflundi Loc: Albuquerque, NM

I'm not Larry, but ...

The formula that Larry gave is known as the "thin-lens formula." It describes how the light travels through an "ideal" lens consisting of a single thin element. In that case, the object distance is measured from the object you are focusing on and the middle of the element and the image distance from the middle of the element to the sensor. In this ideal case, the object distance + the image distance equal the distance from the sensor to the object.

Real life photographic lenses are thin though, but the thin-lens formula still works pretty well as an approximation. To be more accurate for real lenses, you measure the object distance to the "entrance pupil" and the image distance from the "exit pupil". Those locations depend on the lens design but you could roughly approximate them by assuming the front element and rear element surfaces. As you can see, the object distance + the image distance does *not* equal the distance from the sensor to the object, but is close except for object distances that are close to the lens.

larryepage Loc: North Texas area

Afundi correctly points out that for complex lens systems, some adjustments must bemade to the thin lens formula. For some systems, it is possible to identify an "optical center" somewhere in the lens that can be used as the basis of calculations. Some require a center for the object end and a different center for the image end. Some may require a still different treatment. I don't necessarily agree that you can use the back element of the lens to determine image distance, especially for telephoto lenses.

G Brown Loc: Sunny Bognor Regis West Sussex UK

on a prime lens your start point is the mark on the camera that equals the sensor position in the camera (>l marked similar to this) to the stated minimal FP of the lens( ie 10mm is from the sensor point to the object.)

BboH Loc: s of 2/21, Ellicott City, MD

[quote=larryepage]The lens formula is, in fact, very simple.

There is also a corollary formula that is sometimes helpful, used to compare the image size to the object size:

Magnification = (image distance)/(object distance)

Magnification actually is determined by dividing the horizontal width of the sensor by the horizontal width of the angle of view of the lens mm in use.
Ref: Edmund Optics - Image Resource Guide

larryepage Loc: North Texas area

[quote=BboH]
BboH--

You and Edmund are correct that actual magnification is the ratio of the length of any linear feature in the image to the length of that same feature in the object. Many times it is not convenient or possible to measure object features, however. By the rules of congruent triangles, that ratio is the same as the image distance divided by the object distance. It is all part of the same relationship. If the angle of view is used to determine the magnification, it is going to be necessary to use some trigonometric calculations (cosine or secant of the angle of view) to get the final answer. It's a lot easier to just use the ratio of distances, if they can be measured.

jeweler53

Thank you all for your replies! None of them addressed the actual question.

"For example, A 100 mm lens must be 100 mm from the focal plane to focus at infinity. How far must the lens move to focus at 10 feet?"

I am fairly good with math, but I wasn't able to use "infinity" in the equations provided.

Again, Thanks for trying.

BboH Loc: s of 2/21, Ellicott City, MD

Larry
What is confusing to me is what is the difference between the "image" and the "object"? I'm not grasping that distinction.
Thanks

RWR Loc: La Mesa, CA

The formula is:
Length of lens when focused at 10 feet minus length of lens when focused at infinity = how much the lens moved.
Note: For an internal focus lens, it's simpler to figure it in your head.

larryepage Loc: North Texas area

Object distance is the distance from the center (or the optical center) of the lens to the object you are focusing on. Image distance is the distance from the center of the lens to the plane where the image will be formed...the film or the sensor.

John_F Loc: Minneapolis, MN

I must take exception to the last sentence. The object & image distances are measured from the object-side and image-side principal planes. Every lens is an even number of spherical surfaces. Each has a radius and each has center point along the lens axis. The exact position of the centers and values of radius when entered into a mathematical equation will produce 4 cardinal planes and cardinal points by which any series of lens elements may be represented by the simple lens formula, as quoted by larryepage.