Lens / Mirror Combination (Series Optics) Calculator
Build multi-element optical systems from thin lenses and spherical mirrors in series. Trace image formation through each element, compute final image position and magnification, and estimate an equivalent focal length using paraxial optics.
Optical System Configuration
Object Parameters
Positive distance to the left of first element
Optical Elements
+ converging, − diverging
Compare computed image position with a target screen plane
Build a simple multi-element optical system
Stack thin lenses and spherical mirrors in series, set the object distance and focal lengths, and we'll trace images through each element and estimate an equivalent focal length for the whole system.
Try this: Start with two lenses separated by a known distance and see how the final image distance and magnification change.
Understanding Series Optics
Series Optics with Thin Lenses and Mirrors
Many optical instruments—telescopes, microscopes, cameras, and projectors—use multiple lenses and sometimes mirrors arranged in series along a single optical axis. In the paraxial (small-angle) approximation, we can treat each element as an idealized thin element and trace how images form step by step through the system.
The key insight is that the image produced by one element becomes the object for the next element. By chaining these imaging relationships, we can determine where the final image forms and how it compares to the original object in size and orientation.
The Thin Lens / Mirror Equation
1/f = 1/so + 1/si
- f = focal length (positive for converging, negative for diverging)
- so = object distance (positive when object is to the left of the element)
- si = image distance (positive for real image to the right, negative for virtual image)
This equation works for both thin lenses and spherical mirrors in the paraxial regime. For mirrors, the focal length is half the radius of curvature: f = R/2.
Combining Multiple Elements
Two Lenses in Contact
When lenses are touching (separation ≈ 0), their powers add:
1/feq = 1/f1 + 1/f2
Separated Elements
With separation d, the system behavior is more complex. The equivalent focal length depends on f₁, f₂, and d in a nonlinear way.
Element spacing is crucial: a lens pair placed close together behaves like a single element, while larger separations create more complex behavior and can even produce afocal (telescope-like) systems.
Magnification and Image Properties
m = -si/so | Mtotal = m1 × m2 × m3 × ...
- Positive magnification: Image is upright (same orientation as object)
- Negative magnification: Image is inverted (upside-down)
- |m| > 1: Image is larger than the object (magnified)
- |m| < 1: Image is smaller than the object (reduced)
Limitations & Assumptions
This calculator assumes:
- Thin elements (no thickness or principal plane separation)
- Paraxial approximation (small angles near the axis)
- Perfect alignment along a single optical axis
- No aberrations (spherical, chromatic, coma, etc.)
- No aperture effects, vignetting, or diffraction
For real optical design, detailed ray tracing software and aberration analysis are essential. This tool is for educational understanding only.
Lens / Mirror Combination FAQ
Common questions about series optics, image formation, and using this calculator.
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