Lens Equation Calculator Formula
Understand the math behind the lens equation calculator. Each variable explained with a worked example.
Formulas Used
Image Distance
image_distance = 1 / (1/focal_length - 1/object_distance)Magnification
magnification = -(1 / (1/focal_length - 1/object_distance)) / object_distanceVariables
| Variable | Description | Default |
|---|---|---|
focal_length | Focal Length(cm) | 10 |
object_distance | Object Distance(cm) | 30 |
How It Works
Thin Lens Equation
The thin lens equation relates object distance, image distance, and focal length.
Formula
1/f = 1/d_o + 1/d_i
Positive focal length for converging lenses, negative for diverging. Magnification: M = -d_i / d_o. Negative M means inverted image.
Worked Example
An object 30 cm from a converging lens with focal length 10 cm.
- 011/f = 1/do + 1/di
- 021/10 = 1/30 + 1/di
- 031/di = 1/10 - 1/30 = 3/30 - 1/30 = 2/30
- 04di = 15 cm
- 05M = -15/30 = -0.5 (inverted, half size)
Frequently Asked Questions
What does a negative image distance mean?
A negative image distance means the image is on the same side as the object (virtual image). This happens when the object is inside the focal length.
What is a virtual image?
An image that cannot be projected onto a screen. Light rays appear to diverge from the image location but do not actually pass through it.
How does a magnifying glass work?
By placing an object inside the focal length of a converging lens, creating an enlarged virtual image.
Learn More
Guide
Understanding Optics and Lenses
A complete guide to optics and lenses. Learn about refraction, Snell's law, converging and diverging lenses, the thin lens equation, magnification, mirrors, and optical instruments.
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