Cosmic Playground
  • Predict
  • Play
  • Explain

Instructor notes: Telescope Resolution: Sharper Eyes

Public notes (v0.2 policy). Not linked from primary navigation.

Exhibit: /cosmic-playground/exhibits/telescope-resolution/

Overview

Navigation

This guide is instructor-facing Student demo: /play/telescope-resolution/
Main code: apps/demos/src/demos/telescope-resolution/main.ts
Model code: packages/physics/src/telescopeResolutionModel.ts
Data: packages/data-telescopes/src/*

Where to go next

  • Model + math + assumptions: model.md
  • In-class activities (MW + Friday lab + station version): activities.md
  • Assessment bank (clickers + short answer + exit ticket): assessment.md
  • Future enhancements (planning backlog): backlog.md

Why this demo exists

Why This Matters “Bigger telescope” is not just about collecting more light; it is also about seeing finer detail. This demo helps students replace the common “magnification = detail” model with the correct constraint: wave diffraction sets a best-case angular resolution that depends on wavelength and aperture.

This demo is structured as Observable → Model → Inference:

  • Observable: whether two close point sources look like one blur or two distinct peaks.
  • Model: diffraction (Airy pattern) and the Rayleigh criterion scaling $\theta \propto \lambda/D$.
  • Inference: why large apertures, short wavelengths, space telescopes, and interferometry matter for what we can measure.

Learning goals (ASTR 101)

By the end of this demo, students should be able to:

  • Explain why magnification alone cannot reveal more detail beyond a limit.
  • State the qualitative scaling: larger $D$ → smaller (better) $\theta$; longer $\lambda$ → larger (worse) $\theta$.
  • Use “resolved vs unresolved” as a measurement concept (an observational constraint, not a personal failure of eyesight).
  • Give at least one reason radio astronomy uses huge dishes/arrays (long wavelengths).

Learning goals (ASTR 201 stretch)

Students should be able to:

  • Interpret the Rayleigh criterion formula and the meaning of each symbol.
  • Compare resolutions across realistic telescope presets and wavelengths (order-of-magnitude reasoning).
  • Connect “instrument design choices” (e.g., infrared optimization) to the resolution tradeoff.

10–15 minute live-teach script (projector)

  1. Start with the misconception. Ask: “If I keep increasing magnification, can I always see more detail?” Get a show of hands and commit to predictions.

  2. Binary-star test as the observable. Turn on the Binary Star mode. Set a separation where it is clearly resolved, then decrease separation and ask: “At what point do two become one?”

  3. Magnification vs resolution. Change Magnification (zoom). Emphasize: the view changes, but the resolution readouts do not.

  4. Change aperture (holding wavelength fixed). Move the Aperture slider upward and ask students to predict: “Does increasing diameter make the blur bigger or smaller?” Confirm by watching the PSF shrink and the status indicator move toward “resolved.”

  5. Change wavelength (holding aperture fixed). Click the wavelength buttons (visible → IR → radio) and ask: “What happens to resolution at longer wavelength?” Use this to motivate why ALMA-style instruments need large baselines.

  6. Use telescope presets as narrative anchors. Click a few presets (Human Eye → Hubble → Keck/JWST). Ask: “Which change matters most for resolution: being in space, or being big?” Reinforce: space removes atmosphere, but the diffraction limit still depends on aperture and wavelength.

  7. Close with inference language. Say explicitly: “Resolution is a constraint on what we can infer. If two things are unresolved, it doesn’t mean they aren’t there; it means your instrument can’t separate them.”

Misconceptions + prediction prompts

Use these “predict first” prompts to surface wrong models:

  • Misconception: “More magnification = more detail.”
    Prompt: “If magnification were the key, what slider would matter most?” Show that zoom changes the view but aperture/wavelength control the PSF and the resolution readouts.

  • Misconception: “Small telescopes can resolve exoplanets next to stars.”
    Prompt: “What happens when separation is tiny even for large apertures?” Use the status indicator to frame “hard measurement problem.”

  • Misconception: “Radio telescopes can’t see details.”
    Prompt: “Is the problem radio itself, or radio wavelength?” Use wavelength dependence, then introduce interferometry as the workaround conceptually.

Suggested connections to other demos

  • Angular size: reframes “detail” as an angular concept; what matters is how many arcseconds separate features.
  • EM spectrum: wavelength choice is an observing choice; students can connect “what you observe” to “what you can resolve.”

Activities

Navigation

MW Quick (3–5 min)

Type: Demo-driven
Goal: Replace “magnification = detail” with “aperture/wavelength set resolution.”

  1. Open: /play/telescope-resolution/
  2. Leave wavelength at Visible (550 nm).
  3. Ensure Binary star mode is on.
  4. Set a moderate binary separation (so students can see the transition).
  5. Prediction prompt: “If we increase the telescope diameter, should the two stars become easier or harder to separate?”
  6. Increase aperture (e.g., Hubble → Keck). Watch the resolution readout drop and the status move toward resolved.
  7. One-sentence debrief: “Magnification doesn’t change the diffraction limit; $D$ and $\lambda$ do.”

MW Short (8–12 min)

Type: Demo-driven (pairs)
Goal: Practice proportional reasoning with $\theta \propto \lambda/D$.

Student task (pairs)

Fill in the table using presets and wavelength buttons. Record the diffraction limit (arcsec).

Telescope presetWavelengthResolution (arcsec)Better/worse than visible?
Hubble (2.4m)Visible (550 nm)
Hubble (2.4m)Radio (21 cm)
Keck (10m)Visible (550 nm)
Keck (10m)Near-IR ($2.2\,\mu\mathrm{m}$)

Synthesis prompt (2 min): “Why do radio astronomers build arrays instead of a single ‘normal-sized’ dish?”

Friday Lab (20–30+ min)

Type: Demo-driven investigation (small groups)
Goal: Connect physics limit (diffraction) to real observing constraints (atmosphere + AO).

Driving question

“When is a telescope diffraction-limited, and when is it seeing-limited?”

Protocol

  1. Choose one telescope preset (Hubble, Keck, ELT).
  2. For each wavelength button (UV, Visible, Near-IR, Mid-IR, Radio), record:
    • diffraction limit (arcsec),
    • whether the same binary separation is resolved.
  3. Turn on Include Atmosphere and repeat at one wavelength:
    • vary the seeing slider,
    • then turn on Adaptive Optics (AO) and compare.
  4. Write a claim–evidence–reasoning paragraph:
    • Claim: “For ground telescopes, atmosphere often dominates at ____ wavelength unless ____.”
    • Evidence: your recorded resolutions/status changes.
    • Reasoning: connect “blur from turbulence” to what AO is trying to correct.

Station version (6–8 min)

Station card: Telescope Resolution (6–8 minutes) Artifact: a “can this telescope resolve it?” card.

Choose:

  • one telescope preset,
  • one wavelength (UV/Visible/Near-IR/Mid-IR/Radio),
  • one binary separation that is “marginal.”

Record:

  • the resolution (arcsec),
  • the resolved/marginal/unresolved status,
  • one sentence explaining why (link to $\lambda$ and $D$, optionally atmosphere).

Word bank + sanity checks Word bank:

  • Resolution (diffraction limit): the smallest angular separation a telescope can distinguish.
  • Aperture $D$: bigger $D$ → better (smaller) diffraction limit.
  • Wavelength $\lambda$: longer $\lambda$ → worse (larger) diffraction limit.
  • Seeing (atmosphere): turbulence can blur images beyond the diffraction limit; AO can partially correct.

Key relationship (diffraction-limited scaling):

$$\theta \propto \frac{\lambda}{D}$$

Sanity checks:

  • Increasing $D$ should decrease the resolution number (better detail).
  • Increasing $\lambda$ should increase the resolution number (worse detail).
  • With “Include Atmosphere” on, the limit may stop improving unless AO is enabled.

Assessment

Navigation

Clicker questions (with distractors + explanation)

Clicker 1 — What sets resolution?

Demo setup: open /play/telescope-resolution/ (Visible).

Question: In this model, the best-case angular resolution is controlled primarily by:

A. Magnification
B. Aperture diameter and wavelength
C. Exposure time
D. The object’s distance

Correct: B
Why: Diffraction scaling $\theta \propto \lambda/D$.
Misconception targeted: “More magnification = more detail.”

Clicker 2 — Doubling aperture

Demo setup: keep wavelength fixed; change aperture.

Question: If you double the aperture diameter $D$ (same wavelength), the diffraction-limited resolution angle $\theta$:

A. doubles (worse)
B. halves (better)
C. stays the same
D. becomes zero

Correct: B
Why: $\theta \propto 1/D$.
Misconception targeted: “Bigger telescope only collects more light.”

Clicker 3 — Longer wavelength

Demo setup: keep aperture fixed; compare Visible vs Radio (21 cm).

Question: At longer wavelength, resolution becomes:

A. better (smaller $\theta$)
B. worse (larger $\theta$)
C. unchanged
D. unpredictable

Correct: B
Why: $\theta \propto \lambda$.
Misconception targeted: “All light behaves the same for imaging.”

Clicker 4 — Space vs ground

Demo setup: compare with and without Include Atmosphere.

Question: Turning on the atmosphere mainly demonstrates:

A. Space telescopes are diffraction-limited; ground telescopes can be seeing-limited.
B. Space telescopes have larger apertures.
C. The speed of light changes in air.
D. Diffraction disappears in space.

Correct: A
Why: The demo’s “seeing” term can dominate ground-based imaging unless corrected.
Misconception targeted: “Space makes telescopes powerful regardless of aperture.”

Clicker 5 — What does adaptive optics do (in the demo’s story)?

Demo setup: enable Include Atmosphere, then toggle Adaptive Optics (AO).

Question: In this demo’s simplified model, AO mainly:

A. makes wavelength shorter
B. increases aperture diameter
C. reduces the effective blurring from the atmosphere
D. violates the diffraction limit

Correct: C
Why: AO is modeled as reducing the seeing contribution; it does not remove diffraction.
Misconception targeted: “AO lets you beat physics.”

Clicker 6 — Why interferometry?

Demo setup: none.

Question: Astronomers use interferometry (arrays) in radio astronomy mainly because:

A. Radio photons are too weak to detect with one dish
B. Radio wavelengths are long, so a larger effective aperture/baseline is needed for good resolution
C. Radio telescopes can’t be built on Earth
D. Interferometry increases the speed of light

Correct: B
Why: Long $\lambda$ means worse diffraction-limited resolution for a given $D$, so we build larger effective baselines.
Misconception targeted: “Radio just can’t do detail.”

Short-answer prompts

  1. Explain (in words) why magnification has diminishing returns for detail.
  2. Using $\theta \propto \lambda/D$, describe two ways to improve angular resolution.
  3. What problem does Earth’s atmosphere create for images? How does AO try to help?
  4. The demo includes an IR option even though IR has worse diffraction-limited resolution for a given telescope. Give one reason an observatory might still choose IR observations.

Exit ticket (3 questions)

  1. What happens to resolution when $D$ increases (holding $\lambda$ fixed)?
  2. What happens to resolution when $\lambda$ increases (holding $D$ fixed)?
  3. Name one misconception about telescopes that this demo corrects.

Model notes (deeper)

Navigation

Links Student demo: /play/telescope-resolution/
Model code: packages/physics/src/telescopeResolutionModel.ts
UI/visualization code: apps/demos/src/demos/telescope-resolution/main.ts
Dataset: packages/data-telescopes/src/*

What the demo is modeling (big picture)

This demo models the diffraction limit of a circular telescope aperture and uses it to decide whether a “binary star” pair is resolved. The big idea is that resolution is set by wave physics:

  • A point source does not image to a point; it images to an Airy pattern.
  • Two sources are “just resolved” when their Airy patterns are sufficiently separated (Rayleigh criterion).

The core physics utilities live in packages/physics/src/telescopeResolutionModel.ts and are used by the Vite instrument at apps/demos/src/demos/telescope-resolution/.

Units + conventions used in the code

The shared model uses CGS-style internal units for convenience:

  • Wavelength $\lambda$ stored in cm (e.g., 550 nm → $5.5\times 10^{-5}$ cm).
  • Aperture diameter $D$ stored in cm (UI commonly uses meters, then converts).
  • Angular resolution reported in arcseconds.

The implementation computes $\theta$ in radians via $1.22\lambda/D$, then converts to arcseconds using shared unit helpers.

Key relationships to foreground (with meaning + units)

Diffraction limit / Rayleigh scaling

$$\theta = 1.22,\frac{\lambda}{D}$$

Let’s unpack each piece:

  • $\theta$ is the best-case angular resolution (radians).
  • $\lambda$ is wavelength (any length unit).
  • $D$ is aperture diameter (same length unit as $\lambda$).

What this equation is really saying: resolution improves with bigger apertures and worsens with longer wavelengths.

In the demo, this is converted to arcseconds:

$$\theta_{\text{arcsec}} \approx 251643.1,\frac{\lambda(\text{cm})}{D(\text{cm})}$$

Sanity checks

  • Units: $\lambda/D$ is dimensionless, so $\theta$ is in radians ✓
  • Scaling: if $D$ doubles, $\theta$ halves; if $\lambda$ doubles, $\theta$ doubles ✓

Airy pattern (optional deep dive)

The intensity profile for a circular aperture is modeled as:

$$I(x) = \left[\frac{2J_1(x)}{x}\right]^2$$

where $J_1$ is a Bessel function and $x$ is a dimensionless radial coordinate (implemented in the shared model). This is what makes the “rings” and central bright spot.

Assumptions, limitations, and sanity checks

  • Assumes an ideal circular aperture and perfect optics (diffraction-limited performance).
  • Atmospheric effects are modeled with a simple “seeing” term and an optional adaptive-optics toggle (not a full turbulence simulation).
  • The “resolved / marginal / unresolved” labels use ratio cutoffs (didactic thresholds) to support classroom discussion rather than strict instrument performance characterization.

Backlog

Navigation

P0 (blocking / correctness / teachability)

  • Teachability: add a short instructor note that “resolved/marginal/unresolved” thresholds are didactic cutoffs (see packages/physics/src/telescopeResolutionModel.ts) and are not a full instrument-performance model.
  • Atmosphere story: add one explicit “seeing-limited vs diffraction-limited” check step to the activities protocol (students must compare with/without atmosphere).
  • Assessment usability: create a one-slide-per-clicker mini-deck template (prompt + setup + resolution readout) for fast classroom deployment.

P1 (important)

  • Interferometry visualization: add a baseline/array concept mode to connect “effective aperture” to resolution (matches README future ideas).
  • Seeing simulation: replace the single seeing slider with a simple “turbulence animation” toggle (optional) so “blurring” feels less abstract.
  • Real-world comparison gallery: add a small curated set of “what Hubble/JWST/ELT could resolve” examples (avoid made-up numbers; use sourced or omit).

P2 (nice to have)

  • Advanced extensions: PSF fitting / deconvolution mini-explainer; Strehl ratio deeper dive; sparse aperture masking (as optional collapsible deep dive).