Why can the intermediate image look “off” for some slider settings?

Real systems include tube length constraints, field lenses, and aberrations. This page is paraxial and ideal: it is for tracing how the thin-lens algebra chains, not for a commercial instrument spec.

When is |M| ≈ f_obj / f_eye valid?

For a distant object the intermediate image sits near the objective focal plane; with the eyepiece near the standard relaxed-telescope spacing, angular magnification is often quoted as the focal ratio. The page shows that heuristic when the object distance is large compared to focal lengths.

Telescope & Microscope (2 lenses)

Two thin lenses on a common optical axis use the paraxial thin-lens formula twice: the first image distance becomes the object distance for the second lens via u₂ = d − v₁ with lens separation d. Presets approximate a Kepler refractor (positive eyepiece), a Galilean telescope (diverging eyepiece), and a compound microscope (short objective, near object). Rays show the parallel and chief constructions extended through both lenses.

Who it's for: Geometric optics after the single-lens simulator; compares telescope angular magnification ideas with microscope linear magnification.

Key terms

thin lens
telescope
Galileo
Kepler
microscope
magnification

How it works

**Two-lens** paraxial layout: an **object** arrow sends chief and parallel rays through an **objective** and an **eyepiece**. **Kepler** (both converging) inverts the intermediate image; **Galileo** uses a **diverging** eyepiece for an upright view; **compound microscope** uses a **short objective** and a **real intermediate image** between the lenses. Separation **d** is the lens–lens distance along the axis.

Key equations

1/f = 1/u + 1/v (each lens)

u₂ = d − v₁ (intermediate image → second object)

M_total = M₁ M₂ · telescope (distant): |M| ≈ f_obj / |f_eye|

Frequently asked questions

Why can the intermediate image look “off” for some slider settings?: Real systems include tube length constraints, field lenses, and aberrations. This page is paraxial and ideal: it is for tracing how the thin-lens algebra chains, not for a commercial instrument spec.
When is |M| ≈ f_obj / f_eye valid?: For a distant object the intermediate image sits near the objective focal plane; with the eyepiece near the standard relaxed-telescope spacing, angular magnification is often quoted as the focal ratio. The page shows that heuristic when the object distance is large compared to focal lengths.