Enter any two of three values — object distance (x), image distance (y), and focal length (f) — and the Thin Lens Equation Calculator solves for the missing one using 1/f = 1/x + 1/y. You also get the magnification (M) and lens power (P) automatically. Leave the field you want to find blank, and the calculator does the rest.
Focal Length (f)
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Object Distance (x)
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Image Distance (y)
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Magnification (M)
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Lens Power (P)
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Image Type
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Use the thin lens equation: 1/f = 1/x + 1/y, where x is the object distance and y is the image distance from the lens center. Rearranging gives f = (x × y) / (x + y). Simply enter the object and image distances and the calculator will solve for f automatically.
Magnification M is calculated as M = −y / x, where y is the image distance and x is the object distance. A positive M means an upright (virtual) image, while a negative M indicates an inverted (real) image. The absolute value |M| tells you how many times larger or smaller the image is compared to the object.
The thin lens equation 1/f = 1/x + 1/y applies to both converging (convex) and diverging (concave) lenses. The key difference is the sign of the focal length: converging lenses have a positive f, while diverging lenses have a negative f. Sign conventions must be observed consistently.
The power of a lens is P = 1/f, where f is the focal length expressed in meters. Power is measured in diopters (D). A lens with a focal length of 0.5 m has a power of 2 D. Converging lenses have positive power; diverging lenses have negative power.
When the object is placed exactly at the focal point (x = f), the refracted rays emerge parallel to the optical axis and never converge. This means the image is formed at infinity (y → ∞). This principle is used in applications like collimating light beams and spotlights.
A real image forms where refracted light rays actually converge, and it can be projected onto a screen. It occurs when the image distance y is positive. A virtual image forms where rays appear to diverge from behind the lens, cannot be projected, and corresponds to a negative y value.
Yes. For concave lenses, enter the focal length as a negative value (e.g., −10 cm). The thin lens equation works for both converging and diverging lenses as long as you follow the standard sign convention: distances are positive when measured in the direction of the incoming light.
A magnification of 1 (|M| = 1) means the image is the same size as the object. For a converging lens, this occurs when the object is placed at twice the focal length (x = 2f), and the image also forms at twice the focal length on the other side (y = 2f). The image is real and inverted in this case.