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Sandbox Physics

Optics 039 · Imaging, instruments, and visual systems

Ghost Image, Pepper’s Ghost & HUD

An independently initialized three-dimensional apparatus connects Pepper’s Ghost stage, Teleprompter, Automotive head-up display. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelGhost Image, Pepper’s Ghost & HUD
Primary prediction P1\mathcal P_10.500.50
Physical scale P2\mathcal P_250%50\%
Limit check V\mathcal V0.00π0.00\pi
Model regimevalid model regime\text{valid model regime}

Physics tutorial

How to investigate Ghost Image, Pepper’s Ghost & HUD

BackgroundGhost Image, Pepper’s Ghost & HUD is one independently initialized apparatus with three linked investigations: Pepper’s Ghost stage, Teleprompter, Automotive head-up display. Its two controls—Beam splitter reflectance and Plate angle—feed the governing relation Lout=TLscene+RLdisplayL_{\mathrm{out}}=T L_{\mathrm{scene}}+R L_{\mathrm{display}}. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersHow can a tilted combiner place a bright virtual overlay at the right apparent distance?

Start with the essentials

Focus question
How can a tilted combiner place a bright virtual overlay at the right apparent distance?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from Lout=TLscene+RLdisplayL_{\mathrm{out}}=T L_{\mathrm{scene}}+R L_{\mathrm{display}}. Geometry and glow are presentation encodings; the equation, units, conservation or limit check, and validity indicator are the quantitative evidence.

Core mathematical model

Governing relation

Lout=TLscene+RLdisplayL_{\mathrm{out}}=T L_{\mathrm{scene}}+R L_{\mathrm{display}}

The implementation evaluates this relation with dimensional inputs and an executable analytic or numerical benchmark. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Common difficulties

Mistaking glow for measured power

Typical misconceptionA brighter cinematic trail must represent proportionally more optical power.

Better mental modelUse the detector and normalized readouts for comparison. Glow is deliberately nonlinear so weak structure stays visible.

Run the experiment

  1. 01

    Scene 1: Pepper’s Ghost stage

    Select Pepper’s Ghost stage. Sweep Beam splitter reflectance, hold Plate angle fixed, and then reverse the roles. Drag the stage probe to repeat the first sweep directly.

    What to observe: Read the primary prediction, physical scale, limit check, and validity indicator together. Record where the approximation boundary changes.
  2. 02

    Scene 2: Teleprompter

    Select Teleprompter. Sweep Beam splitter reflectance, hold Plate angle fixed, and then reverse the roles. Drag the stage probe to repeat the first sweep directly.

    What to observe: Read the primary prediction, physical scale, limit check, and validity indicator together. Record where the approximation boundary changes.
  3. 03

    Scene 3: Automotive head-up display

    Select Automotive head-up display. Sweep Beam splitter reflectance, hold Plate angle fixed, and then reverse the roles. Drag the stage probe to repeat the first sweep directly.

    What to observe: Read the primary prediction, physical scale, limit check, and validity indicator together. Record where the approximation boundary changes.