Skip to content
Open Model LabInteractive concept
HomeConcept libraryPhysicsOpticsWave Optics
PhysicsOpticsIntermediateStarter track

Concept module

Optical Resolution / Imaging Limits

Image two nearby point sources through one finite aperture and see why diffraction, wavelength, and aperture diameter limit how sharply an optical system can separate them.

Interactive lab

Loading the live simulation bench.

Progress

Not startedMastery: NewLocal-first

Start exploring and Open Model Lab will keep this concept's progress on this browser first. Challenge mode has 2 compact tasks ready. No finished quick test, solved challenge, or completion mark is saved yet.

Let the live model runChange one real controlOpen What to notice

Try this setup

Jump to a named bench state or copy the one you are looking at now. Shared links reopen the same controls, graph, overlays, and compare context.

Saved setups

Premium keeps named exact-state study setups in your account while stable concept links stay public below.

Checking saved setup access.

This concept can keep using stable links while the saved-setups capability resolves for this browser.

Copy current setup

Stable concept and section links stay public below while exact-state setup sharing stays behind premium.

Stable links

Starter track

Step 5 of 50 / 5 complete

Wave Optics

Earlier steps still set up Optical Resolution / Imaging Limits.

1. Polarization2. Diffraction3. Double-Slit Interference4. Dispersion / Refractive Index and Color+1 more steps

Previous step: Dispersion / Refractive Index and Color.

Start from track beginning

Why it behaves this way

Explanation

An imaging system does not send each object point to a mathematically perfect point on the detector. A finite aperture diffracts the light, so each point becomes a blur pattern with a finite width.

This page keeps that story bounded on purpose: two equal point sources, one finite lens aperture, and one detector strip. The same wavelength, aperture diameter, point separation, and detector sample drive the stage, the profile graph, the overlays, the worked examples, the prediction prompts, the challenge checks, and the quick test so imaging limits stay tied to one honest diffraction-limited picture instead of a giant Fourier-optics platform.

Key ideas

01Resolution is limited because finite apertures diffract light. Even a well-focused lens turns one point into a spread pattern with a nonzero width.
02A larger aperture improves resolution by shrinking the diffraction blur, while a longer wavelength worsens resolution by broadening it.
03The Rayleigh limit theta_R approximately equals 1.22 lambda / D for a circular aperture, so two points become harder to distinguish when their angular separation falls below that scale.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough
Use the current aperture-limited imaging state directly. These substitutions stay attached to the live detector profile instead of switching to a detached worksheet.

Premium unlocks saved study tools, exact-state sharing, and the richer review surfaces that support this guided flow.

View plans
Frozen valuesUsing frozen parameters

For the current wavelength lambda = 550 nm and aperture D = 2.4 mm, what Rayleigh limit follows for two equal point sources?

Wavelength

550 nm nm

Aperture diameter

2.4 mm mm

Rayleigh limit

0.28 mrad mrad

1. Start from the Rayleigh estimate

Use for a circular aperture.

2. Substitute the live wavelength and aperture

\theta_R \approx 1.22 \dfrac{550 nm}{2.4 mm} = 0.28 mrad.

3. Map that blur scale onto the detector

With the fixed focal length, the same limit maps to an image-plane blur radius of 33.55 um.

Current Rayleigh limit

and .
The current pair is at or above the Rayleigh threshold, so the detector profile can sustain a visible dip between the peaks.

Common misconception

If the lens is focused correctly, two nearby points should always stay perfectly separate.

Correct focus removes defocus blur, but it does not remove diffraction from a finite aperture.

That is why nearby points can still merge when the aperture is small or the wavelength is long, even in an otherwise ideal imaging setup.

Mini challenge

You cannot move the object points, but you want the detector profile to show a clearer split. What is the best optical move?

Make a prediction before you reveal the next step.

Choose whether you should change aperture, wavelength, or detector sample position.

Check your reasoning against the live bench.

Increase the aperture or use a shorter wavelength so the diffraction blur shrinks.
Moving the detector sample only reads a different place on the existing image. The actual resolution limit changes when the aperture diameter or wavelength changes the diffraction width itself.

Quick test

Variable effect

Question 1 of 4

Answer from the live diffraction-limited imaging story, not from detached slogans.

Which change most directly improves resolving power for the same wavelength and object spacing?

Use the live bench to test the result before moving on.

Accessibility

The simulation shows two distant point sources on the left, one finite lens aperture in the middle, and one detector strip on the right. Each source sends light through the same aperture, and the detector strip brightens according to the combined diffraction-limited image profile.

Optional overlays show the aperture diameter on the lens, the current point-spread centers on the detector, and the Rayleigh blur scale around those centers. A movable detector sample marks one position on the strip and reports the current normalized exposure there.

Graph summary

The graph shows normalized exposure against detector height, with one combined profile and two dashed component profiles for the individual point-spread contributions.

Hovering the graph previews the matching detector position on the stage, so the spatial profile stays linked to the same image plane rather than turning into a detached time plot.