# FUNDAMENTAL LENS EQUATION EXPLAINED

Topic:
Logarithm
Trying to figure out how images are formed in various situations? The most efficient way to cope with the task is to use the Fundamental Lens Equation. It provides info about the interdependence between an object distance, an image distance, and the focal length in a straightforward quantitative way.  Ray TracingRay Tracing is a widely appreciated technique that allows defining the image size, location, type of image that is created by objects when they are placed at a particular distance from the lens. You can rely on this method if you want to get accurate information about an object and the image it forms. However, Ray Tracing is of no help if you need the results to be presented in a quantitative way. If you are aimed at getting the numeric info, you need to resort to the Fundamental Lens Equation that grounds on the geometric studying of ray tracing of thin lenses. This way, you can perform quantitative analyses of good lenses and cameras, and delve into the world of optical illusion photographyConvex and Concave LensesA thin lens is the one with thickness needed for the rays to refract. However, using such a lens, you won’t see such phenomena as dispersions and aberrations.Before getting down to physics optics equations, you should understand that there are 2 main types of lenses – convex and concave. The former has a thicker center and thinner edges. Concave lenses are constructed in the opposite way. When you use a convex lens and direct a light beam through it, you’ll get the light focused on the other side of the lens in one point, known as a focal point. Concave lenses work in a different way, namely, they condense light. Thus, the focal point is shifted to the front of the lens. In fact, it is represented as a point on the axis of the incoming light, which seems to scatter the light beam through the lens. Lens EquationWe can describe the image “build” by a convex lens in a numeric way using such optics equation – 1/x + 1/y = 1/f.
• x marks the distance between the object and the center of the lens
• y indicates the distance between the image and the center of the lens
• f refers to the focal length of the lens measured in length units
Using this equation, you can easily and accurately define the image distance, height and orientation if you use convex lenses and the X is greater than F. The same equation is applicable if you need to calculate the distance both for real and virtual images. It also gives correct results when used for positive and negative lenses.Using concave lenses, you always end up with upright, virtual images. Though the lens equation is identical, the value of f is changed to negative.Example. What image will you get if you place an object at the distance of 14 cm from a convex lens with a focal length of 7 cm?In this case x = 14 cm and f = 7 cm. If we use the Fundamental Lens Equation and replace unknown with these numbers, we’ll learn that y = 14 cm. Not to make mistakes while using this equation for thin lenses, you need to adhere to the following sign conversion:
• f is positive for a converging lens and negative for a diverging lens.
• y is positive if an image is real (the image is on the opposite side to the object) and is negative in the case of a virtual image.
Real vs Virtual Images Conventionally, we can divide images into 2 types – real and virtual. Real images appear as a result of light convergence and reaching the focus. The simplest sample is a projector. It handles light in such a way that it forms a real image on the screen.Virtual images are perceived images, so you can see them but can’t touch them. These images are formed by rays that never converge. Thus, you can’t use a screen to show virtual images. A great example is a magnifying glass.