What is the thin lens equation?

The thin lens equation is 1/f = 1/do + 1/di, where f is the focal length, do is the object distance from the lens, and di is the image distance. It applies to thin converging (convex) and diverging (concave) lenses when the lens thickness is negligible compared to the focal length and object/image distances. Positive values of di indicate real images formed on the opposite side, while negative values indicate virtual images on the same side as the object.

What is magnification in optics?

Magnification (m) is the ratio of the image height to the object height, calculated as m = -di/do. A positive magnification means the image is upright relative to the object, while a negative magnification means it is inverted. An absolute magnification greater than 1 means the image is enlarged, less than 1 means it is reduced, and exactly 1 means same size. Lateral magnification applies to the height dimension perpendicular to the optical axis.

What is the difference between a real and virtual image?

A real image forms where light rays actually converge after passing through a lens, on the opposite side from the object. It can be projected onto a screen and has a positive image distance. A virtual image forms where light rays appear to diverge from, on the same side as the object. It cannot be projected onto a screen and has a negative image distance. Converging lenses can form both types, while diverging lenses always form virtual images.

How do converging and diverging lenses differ?

Converging (convex) lenses are thicker at the center and bend parallel light rays inward to a focal point. They have positive focal lengths and can produce real or virtual images depending on object placement. Diverging (concave) lenses are thinner at the center, spread parallel light rays outward, have negative focal lengths, and always produce virtual, upright, reduced images regardless of object position.

What happens when an object is placed at the focal point of a converging lens?

When an object is placed exactly at the focal point of a converging lens, light rays exit parallel to each other and never converge. The image forms at infinity and the magnification is theoretically infinite. In the thin lens equation, 1/di becomes zero, meaning di approaches infinity. This principle is used in collimators and spotlights where a parallel beam of light is desired.

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Calculate image distance, focal length, or object distance using the thin lens equation. Get magnification, image type, and orientation instantly.

Understanding the Thin Lens Equation

The thin lens equation (1/f = 1/d_o + 1/d_i) is one of the most fundamental relationships in geometric optics. It connects the focal length of a lens to the distances of the object and its image. First formalized in the 17th century, this equation remains essential for designing cameras, telescopes, microscopes, eyeglasses, and countless other optical instruments. The equation assumes that the lens is thin enough that all refraction occurs at a single plane, which is an excellent approximation for most everyday lenses.

This calculator lets you solve for any one of the three variables: focal length, object distance, or image distance. It also computes the magnification (m = -d_i/d_o), which tells you how large the image is relative to the object and whether it is upright or inverted. The sign conventions used here follow the standard physics convention: positive image distances correspond to real images, and positive focal lengths correspond to converging lenses.

Real vs. Virtual Images

A real image forms when light rays actually converge at a point after passing through the lens. Real images have positive image distances and can be projected onto a screen. A virtual image forms where diverging rays appear to originate; it has a negative image distance and cannot be captured on a screen but can be seen by looking through the lens. Converging lenses produce real images when the object is beyond the focal point, and virtual images when the object is between the lens and the focal point.

Magnification and Image Characteristics

The magnification tells you three things about the image: its size relative to the object (|m| > 1 means enlarged, |m| <1 means reduced

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Disclaimer: This calculator is for informational and educational purposes only. Results are estimates and should not be considered professional expert advice. Consult a qualified professional before making decisions based on these calculations. See our full Disclaimer.

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