Optics 009 · Ray worlds, boundaries, and natural optics

Window Ghost Observatory

Why does window glass barely shift the view through it, yet show ghost images at night? The two faces are parallel, so the bend on the way out undoes the bend on the way in; the glass thickness only shifts the ray sideways. Each glass surface also reflects about 4 percent of the light. A double-pane window has four surfaces, and at night, with no daylight coming through, their faint reflections of the bright room show up as ghosts. An anti-reflection coating weakens them.

This three-dimensional apparatus has these scenes: Parallel but not collinear, Four-surface night ghosts, Bare versus AR-coated ghosts. Adjust two controls with physical units or drag the probe directly; the detector trace and three quantitative checks are recalculated from the equation on the page.

Primary prediction

\mathcal P_1

$0.50$

Physical scale

\mathcal P_2

$50\%$

Limit check

\mathcal V

$0.00\pi$

Model regime $\text{valid model regime}$

This Lab states the approximation it uses and runs an analytic or numerical benchmark against it. Scene sizes and glow are for display only; judge the physics from the equation, the readouts with units, the benchmark check and the validity indicator.

Physics tutorial

Audit the physics of Window Ghost Observatory

BackgroundLight crossing a flat, lossless window refracts twice, and the two bends are equal and opposite. The beam comes out shifted sideways, measured perpendicular to its direction, by exactly $d=t\,\frac{\sin(\theta_i-\theta_t)}{\cos\theta_t}$ . The same two surfaces also reflect part of the power, as the Fresnel equations describe. A double-pane window has four such surfaces, so a lamp at night can reach your eye along four complete paths from lamp to window to eye, each slightly different.

Why it mattersWhy does window glass barely shift the view through it, yet show ghost images at night?

Start with the essentials

Focus question: Why does window glass barely shift the view through it, yet show ghost images at night?
One-sentence intuition: Parallel does not mean on the same line. When the entrance and exit faces are parallel, $\theta_{\mathrm{out}}=\theta_i\quad\text{but}\quad d\ne0$ . Thickness changes how far apart the two lines are, not the final direction. Every ghost the Lab draws includes the reflection that created it and every transmission along its way.

Core mathematical model

Exact sideways shift through a parallel plate

n_{\mathrm a}\sin\theta_i=n_{\mathrm g}\sin\theta_t,\qquad d=t\,\frac{\sin(\theta_i-\theta_t)}{\cos\theta_t}

The shift is measured perpendicular to the two parallel rays in air. It is zero at normal incidence and grows with the plate thickness and with the incidence angle.

Primary reflections from the four surfaces

P_j^{(q)}=R_q\left(1-R_q\right)^{2j},\qquad q\in\{s,p\},\quad j=0,1,2,3

Light reflected from a deeper surface passes through every surface in front of it twice, once going in and once coming out. The unpolarized power shown is the average of the two polarization channels.

Transmitted ghosts from round trips inside the glass

P_k^{(q)}=\left(1-R_q\right)^2R_q^{2k},\qquad \sum_{k=0}^{\infty}P_k^{(q)}=\frac{1-R_q}{1+R_q}

Each extra round trip adds two reflections and shifts the emerging beam sideways by two more crossings of the glass. Summed incoherently to infinity, these ghosts and the reflected beams together conserve energy.

Common difficulties

Drawing a ghost without the reflections that made it

Typical misconceptionYou can put a faint copy beside the main transmitted ray without tracing how it entered, reflected inside and left the glass.

Better mental modelSuch a copy has no optical history, so it cannot predict where the ghost lands or how strong it is. Here every colored ghost is one continuous path that obeys Snell's law at each surface. Its width shows the Fresnel power on a nonlinear scale, and the power itself is reported separately.

Run the experiment

01
Scene 1: Parallel but not collinear
In the first scene, set the plate to minimum thickness and sweep the incidence angle from normal up to its limit, then increase the thickness. Compare the green output with the dashed no-glass line and read the pink perpendicular bracket.
What to observe: The ray leaves at exactly the angle it came in, because the second refraction undoes the first. It is still shifted, because inside the glass it traveled at a different slope.
02
Scene 2: Four-surface night ghosts
In the night-window scene, orbit until all four reflection paths from the panes are visible. Sweep incidence and thickness, and watch the four angular peaks separate while the deeper paths lose power passing through the surfaces in front.
What to observe: At normal incidence the four angular peaks overlap, although all four paths still carry power. Viewing at an angle separates them. The back surface of a pane can look almost as bright as its front, because both Fresnel transmissions on the way are still close to one.
03
Scene 3: Bare versus AR-coated ghosts
Compare the bare and coated lanes, stacked one above the other. Follow the main ray, the one-round-trip ghost and the two-round-trip ghost all the way through both faces, then compare the detector profiles and the suppression readout.
What to observe: The first transmitted ghost sits two internal sideways crossings away from the main ray. A round-trip ghost scales with the square of the surface reflectance, so lowering the reflectance suppresses it strongly. That is why the secondary peaks almost vanish on the coated detector trace.