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How to Form an Image with an Optical Lens Setup

Although a common misconception, individual optical lenses do not always form an image when the object plane is placed a focal length away from the lens. Rather, image location is dependent on object location. Join Monica Rainey, Optical Engineer, as she explains focal length and how to form an image with three simple real-world optical lens setups.

Hi, I am Monica, an Optical Engineer here at Edmund Optics. Today, I would like to talk about the meaning of focal length of a lens and how to determine where an image will form when using a single lens. There is a common misconception that individual lenses will always form an image a focal length away from the lens. This is not necessarily true as the image location depends on the object location. For an example, we'll consider an object passing through one single positive lens and forming an image on the other side. In this setup, our object is a USAF resolution target and the lens has a 50mm focal length. If we call the distance from the object to the lens, Z, the distance from the lens to the image plane, Z prime, and the focal length of the lens, F, we can use this equation to determine where the image will form or what focal length lens we need. In this equation, n prime is the refractive index of the medium between the lens and the image plane, and n is the refractive index of the medium between the object and the lens. Typically, we are working in air, so n and n prime both equal 1. For this equation, we are assuming the lens is thin, meaning the diameter of the lens is about 10 times larger than its thickness. Also, we use a sign convention here that dictates that we write a distance measured to the left as a negative number, so Z would be negative for the case shown here. This equation governs where an image will form. You can choose any two of the variables and solve for the third when setting up your imaging system. I would like to illustrate three different scenarios for you using this object. As you can see in the first setup, if the object you are trying to image is closer to the lens than the focal length of the lens, in our case, 50mm, an image of the object will not form. In this second setup, once the lens is at least one focal length away from the object, an image will form as governed by the equation I just described. In this case, we will move the lens to be 70mm from the object, so an image will form 175mm away. You can see that as we move the lens the distance to the image also changes. The light does not always focus at one focal length away from the lens. As seen in this final setup, I am using a laser source for collimated light. Collimation means that all of the light rays are travelling parallel to each other, not converging or diverging. The image will form at a distance equal to the focal length of the lens. Once the lens is far enough away from the object, about 10 times the focal length of the lens, we can consider it to be collimated. I hope this answers some of your questions about finding the image from a single lens. You can browse more of our technical application notes and videos to learn more key concepts and find answers to common questions on our website.