Calculate Lens Equation
Online calculator and formulas for calculating focal length, object distance and image distance
Lens Equation Calculator
Imaging Law
Calculates the missing optical imaging parameter: Focal length (f), Object distance (g) or Image distance (b).
Example Calculations
Example 1: Calculate image distance
Problem:
An object is 30 cm in front of a converging lens with focal length 10 cm. How far is the image from the lens?
Given:
- Object distance: g = 30 cm
- Focal length: f = 10 cm
- Find: Image distance b
Solution:
Lens equation:
\[\frac{1}{f} = \frac{1}{g} + \frac{1}{b}\]Example 2: Calculate object distance
Problem:
A lens with focal length 8 cm produces an image at distance 24 cm. How far was the object?
Given:
- Focal length: f = 8 cm
- Image distance: b = 24 cm
- Find: Object distance g
Solution:
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Formulas of the lens equation
The lens equation (also called imaging law) describes the relationship between focal length, object distance and image distance of an optical lens. It is one of the most fundamental equations of geometric optics.
Lens equation (Imaging law)
The fundamental equation for optical imaging.
g = Object distance [cm]
b = Image distance [cm]
Magnification
Size ratio of image to object.
B = Image size, G = Object size
Calculate image distance
Rearrangement to calculate image distance.
Calculate object distance
Rearrangement to calculate object distance.
Calculate focal length
Rearrangement to calculate focal length.
Important Rules
- Converging lens (convex lens): f > 0. Produces real, inverted images when g > f.
- Diverging lens (concave lens): f < 0. Produces only virtual, upright, reduced images.
- Focal point: When g = f, then b = ∞ (image at infinity).
- 2f point: When g = 2f, then b = 2f (image same size as object).
- Virtual images: Occur when g < f (magnifying glass effect).
Detailed description of the lens equation
Physical Fundamentals
The lens equation describes how a lens images an object. It is the central tool of geometric optics and is used in numerous applications.
Focal length (f): The distance from the lens center to the focal point, where parallel incident rays are focused. Converging lenses have positive, diverging lenses have negative focal lengths.
Object distance (g): The distance between the object and the lens center.
Image distance (b): The distance between the produced image and the lens center.
Usage Instructions
Select with the radio buttons which parameter should be calculated. Enter the two known values and click "Calculate". All values are in centimeters.
Application Areas
Photography and Cameras
Calculation of focal lengths, focus distance and image size. Lens design for various focal lengths.
Microscopy and Telescopes
Design of lens systems, calculation of magnifications and depth of field for observation instruments.
Projectors and Displays
Calculation of projection distance, lens size and image size for optical systems.
Medical Devices
Endoscopes, surgical microscopes, laser eye surgery and other optical diagnostic and treatment systems.
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