Three-Element Optical System: Convex Lens, Concave Lens, and Rotated Prism

We visualize an optical system made of two lenses and a prism. The convex lens has focal length $f_1 = +50\,\text{cm}$, the concave lens has focal length $f_2 = -46\,\text{cm}$, and the prism is shown as a triangular element rotated by $90^\circ$.

How the system is represented

1. Convex lens converges parallel light rays toward its focal region.
2. Concave lens diverges rays, partially canceling the convergence from the first lens.
3. Prism rotated by 90° bends the beam direction instead of focusing it, so the outgoing ray changes angle.

Optical idea

For thin lenses placed close together, the effective optical power is approximately:

$$\frac{1}{f_{\text{eq}}} = \frac{1}{f_1} + \frac{1}{f_2}$$

Using the given signs:

$$\frac{1}{f_{\text{eq}}} = \frac{1}{50} - \frac{1}{46}$$

This means the combined lens pair is weak overall and slightly divergent.

The prism is then modeled as a directional deflector: it does not use a focal length, but instead rotates the beam path. In the animation, you can adjust the ray bundle angle, prism strength, and observe how the path changes through the system.

What to observe

• Incoming parallel rays start on the left.
• The convex lens bends them inward.
• The concave lens spreads them back outward.
• The prism rotates the beam direction by 90° and sends it upward or downward depending on the selected orientation.

This makes the visualization useful for understanding how mixed optical elements combine geometrically rather than as a single lens formula alone.