Melles Griot Optics Guide

Examples

Conjugate Distances and Magnification

With a real lens of finite thickness, the image distance, object distance, and focal length are all referenced to the principal points, not to the physical center of the lens. By neglecting the distance between the lens' principal points, known as the hiatus, s + s" becomes the object-to-image distance. This simplification, called the thin-lens approximation, can speed up calculation when dealing with simple optical systems. A simple graphical method can also be used to determine paraxial image location and magnification. This graphical approach relies on two simple properties of an optical system. First, a ray that enters the system parallel to the optical axis crosses the optical axis at the focal point. Second, a ray that enters the first principal point of the system exits the system from the second principal point parallel to its original direction (i.e., its exit angle with the optical axis is the same as its entrance angle). This method has been applied to the three examples illustrated below. Note that by using the thin-lens approximation, this second property reduces to the statement that a ray passing through the center of the lens is undeviated. Object Outside Focal Point A 1-mm-high object is placed on the optical axis, 200 mm left of the left principal point of a 01 LDX 103 (f = 50 mm). Where is the image formed, and what is the magnification? (See figure below)

(or real image is 0.33 mm high and inverted).

Object outside focal point (f=50 mm, s = 200 mm, s "= 66.7 mm)
Object Inside Focal Point The same object is placed 30 mm left of the left principal point of the same lens. Where is the image formed, and what is the magnification? (See figure below.)

In this case, the lens is being used as a magnifier, and the image can be viewed only back through the lens.

Object inside focal point (f = 50 mm, s = 30 mm, s" = -75 mm)
Object At Focal Point A 1-mm-high object is placed on the optical axis, 50 mm left of the first principal point of an 01 LDK 019 (f = 50 mm). Where is the image formed, and what is the magnification? (See figure below.)

The virtual image is 0.5 mm high and upright.

Object at focal point (f = -50 mm, s = 50 mm, s" = -25 mm)

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