The Thin Lens Equation

The thin lens equation is a fundamental principle in geometric optics that relates the focal length of a lens to the distances of the object and the image from the lens. It provides a simple, yet highly accurate model for understanding how lenses form images.

The equation is:

• $f$: Focal Length. The distance between the center of the lens and its focal point. It is positive for converging (convex) lenses and negative for diverging (concave) lenses.
• $d_o$: Object Distance. The distance from the object to the center of the lens. This is almost always taken as a positive value.
• $d_i$: Image Distance. The distance from the image to the center of the lens. A positive value indicates a real image (formed on the opposite side of the lens), while a negative value indicates a virtual image (formed on the same side as the object).

How to Use This Calculator

1. Select Variable: Use the selector buttons at the top to choose which variable you need to calculate: Focal Length ($f$), Object Distance ($d_o$), or Image Distance ($d_i$).
2. Enter Known Values: Based on your selection, the calculator will dynamically display the two required input fields. Enter the known distances (in meters, ‘m’).
3. Apply Sign Convention: It is crucial to use the correct signs according to the physics convention:
   • $f$ (Focal Length): Positive for converging (convex) lenses, Negative for diverging (concave) lenses.
   • $d_i$ (Image Distance): Positive for real images, Negative for virtual images.
4. Calculate: Click the “Calculate” button.
5. View Result: The calculated value and the substituted equation will appear in the Result box, rendered in real-time using LaTeX for clarity. The result will be in meters (m).