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Sandbox Physics

Optics 021 · Imaging, instruments, and visual systems

Thin Lens Imaging Bench

A signed thin-lens bench ties three principal rays, draggable object position, focal markers, image orientation, projectable-screen eligibility, and the full conjugate curve to one first-order ray-transfer law.

Interactive modelThin Lens Imaging Bench
Signed image distance s′s'0.500.50
Lateral magnification mm50%50\%
Lens-equation residual ∣Δlens∣\left|\Delta_{\mathrm{lens}}\right|0.00π0.00\pi
Model regimevalid model regime\text{valid model regime}

Physics tutorial

Audit the physics of Thin Lens Imaging Bench

BackgroundAn ideal thin lens collapses all refraction into one plane. With real object distance positive, its signed conjugates obey 1f=1s+1s′\frac{1}{f}=\frac{1}{s}+\frac{1}{s'}. Positive image distance means physical rays meet on the far side; negative image distance means only their backward constructions meet on the object side.

Why it mattersHow do three principal rays locate every real and virtual thin-lens image?

Start with the essentials

Focus question
How do three principal rays locate every real and virtual thin-lens image?
One-sentence intuition
Image orientation and size are not visual choices. They follow the signed magnification m=h′h=−s′sm=\frac{h'}{h}=-\frac{s'}{s}. A screen can intercept a real image, but moving a screen cannot turn a virtual construction into emitted light.

Core mathematical model

Signed conjugate equation

1f=1s+1s′\frac{1}{f}=\frac{1}{s}+\frac{1}{s'}

Here s is positive for a real object, f is positive for a converging lens, and s prime is positive only for a real image on the opposite side.

Ideal ray kick

uout=uin−yfu_{\mathrm{out}}=u_{\mathrm{in}}-\frac{y}{f}

Every displayed ray is propagated to its actual height y on the lens plane and receives this first-order slope change. Independent launch heights therefore meet at one Gaussian conjugate.

Lateral magnification

m=−s′sm=-\frac{s'}{s}

Negative magnification is inverted. A converging lens inside focus and every diverging lens in this experiment produce positive, upright virtual images.

Common difficulties

Letting a virtual image emit rays

Typical misconceptionOnce a translucent image marker is drawn, rays may originate there and travel through the lens.

Better mental modelOnly solid paths after the lens are physical. Dashed paths run backward from those same outgoing rays and are explicitly construction lines; no energy propagates along them.

Run the experiment

  1. 01

    Scene 1: Converging real image

    Start with the real-image scene. Drag the object through two focal lengths and compare the moving screen, signed image distance, and inverted arrow.

    What to observe: At s equals twice f, image distance equals twice f and magnification is minus one. Crossing that object position swaps reduction for enlargement without changing real-image orientation.
  2. 02

    Scene 2: Inside-focus virtual image

    Enter the inside-focus scene and approach the focal point from below. Watch the backward construction intersection retreat while the physical rays become nearly parallel.

    What to observe: At the focal boundary the three outgoing slopes become parallel and no finite screen position can collect a point image. The interface reports the singularity instead of clipping infinity into a fake focus.
  3. 03

    Scene 3: Diverging-lens image

    Switch to the diverging lens and sweep object distance. Verify that the virtual image remains between the lens and its front focus.

    What to observe: For negative f, image distance and magnification keep their virtual-upright signs over the entire positive object-distance range.