What Is the Thin Lens Equation?
The thin lens equation describes how a lens forms an image. It connects three quantities: the focal length f of the lens, the distance from the object to the lens dₒ, and the distance from the lens to the image dₕ. This calculator solves for the image distance and the magnification, so you can predict where an image will appear and whether it is enlarged, reduced, upright, or inverted.
How to Use It
Enter the focal length and the object distance using consistent units (centimeters are common in optics problems). A converging (convex) lens has a positive focal length; a diverging (concave) lens has a negative focal length. The calculator returns the image distance and the magnification automatically.
The Formula Explained
The governing relationship is 1/f = 1/d_o + 1/d_i. Rearranged to find the image distance:
The magnification is
A positive d_i means a real image forms on the opposite side of the lens; a negative d_i means a virtual image forms on the same side as the object. A negative M indicates an inverted image, while a positive M indicates an upright image.
Worked Example
Suppose a converging lens has f = 10 cm and an object sits at d_o = 30 cm. Then
so d_i = 15 cm. The magnification is M = -15/30 = -0.5, meaning the image is real, inverted, and half the size of the object.
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