How to Determine Magnification of an Optical Lens Setup

Hi, I am Monica, an Optical Engineer here at Edmund Optics. Today, I want to talk about one of the common questions we get from customers. When doing basic imaging, how do you determine the magnification a single lens will provide? A common misconception is that magnification is a property of the lens itself, when in reality, it is a result of how the system is laid out. To illustrate this point, we've setup a simple imaging system. Here, we have an object, single lens and image plane. With this system, we know we can apply the imaging equation shown here. We recall that n prime and n both equal 1 since we are in air and we know z is negative according to our sign convention since we measure it from right to left. For further detail on the imaging equation, please watch the video linked in the text below. The magnification can be found by taking the ratio of the image distance to the object distance. A negative magnification indicates the image will be inverted. A positive magnification indicates the image will be upright. Since we have a negative distance and a positive distance for our setup here, we have an inverted image, which you can see here. This equation can be solved to find the magnification of a given system, or to find the object and image distance required to achieve the desired magnification. We can also use this equation, along with the imaging equation, to determine the focal length of a lens needed to meet the requirements of a system. You can see these equations are tied to each other, so it is not possible to independently select object distance, image distance and magnification. Since we now know that magnification is the ratio of image to object distance, we can determine where our lens need to be if we want to focus the source down to be smaller or expanded to be larger. If you want to make your source or object larger, with a magnification greater than 1, the lens must be closer to your object than the image, since image distance must be greater than your object distance. However, recall from our previous video, that if your object is closer to the lens than its focal length, an image will not form. If you want to focus your object down to be smaller, with a magnification less than 1, the lens must be closer to your image than the object since the object distance must be greater than the image distance. Often times, we are also asked about the magnifying power of a lens. For example, you might need 3x magnification for an inspection application. Again, magnification is not a property of the lens itself but of how it is used in the system. However, there is an easy rule of thumb to help you determine the magnification for a hand-held magnifier. Magnifying power can be determined when the lens is at the near point of your eye, which is about 10 inches or 250mm in front of the eye. To find the approximate magnifying power, divide the 250mm near point length by the focal length of the lens in mm as shown in this equation. For example, a 25mm focal length lens provides magnifying power of approximately 10x when held near the eye. However, remember that this is only valid when using a lens with the human eye as the magnifier, not in an optical bench setup. I hope this helps you in understanding magnification. 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.