PhysicsSolver360 logoPhysicsSolver360°
Powered by Solver360°

Angular Resolution Calculator

Find minimum resolvable angle using Rayleigh criterion θ = 1.22λ/D

Parameters

nmⓘ
mⓘ
Show Trail

Controls

xⓘ

Calculated Values

Angle:
0.00;rad0.00;rad
Angle:
1.38;arcsec1.38;arcsec

Examples

λ=550 nm, D=0.1 m

Small telescope.

    Visualization

    Angular Resolution (Rayleigh Criterion)

    Wave diffraction limits how close two point sources can be resolved. For a circular aperture of diameter D, Rayleigh criterion: θ ≈ 1.22 λ/D (radians), where θ is minimum resolvable angular separation.

    Smaller θ means better resolution. Large telescopes need large D to resolve stars; radio telescopes use long λ but huge dishes. Human eye pupil ~2–5 mm limits resolution to ~1 arcminute.

    In arcseconds: θ(arcsec) ≈ 0.252 λ(μm)/D(m) approximately. Hubble (D = 2.4 m) at 550 nm gives θ ≈ 0.05 arcsec (before atmosphere).

    Microscopes use numerical aperture NA instead: θ ≈ 0.61 λ/NA. Resolution also depends on contrast and detector noise.

    Rayleigh assumes equal-intensity sources; Sparrow criterion is slightly less strict. Diffraction limit is fundamental, not a manufacturing defect.

    Key Concepts

    • θ = 1.22 λ/D
    • Radians vs arcsec
    • Larger D → better resolution
    • Diffraction limit
    • NA in microscopes

    Real-World Applications

    • Telescope design
    • Microscopy resolution
    • Radio astronomy dishes
    • Camera pixel pitch vs lens
    • Class 12 resolving power

    Explore Further

    More optics tools

    • Snell's Law

      Calculate refraction angles and analyze light behavior at media boundaries.

    • Magnification

      Calculate linear and angular magnification for optical systems.

    • Thin Lens Equation

      Find image distance and magnification using 1/f = 1/u + 1/v.

    • Spherical Mirror Equation

      Calculate image position and magnification for concave and convex mirrors.

    • Lens Power

      Convert focal length to diopters and combine thin lens powers.

    • Critical Angle

      Find critical angle for total internal reflection between two media.

    Physics Equations

    Rayleigh:
    θ=1.22λD\theta = 1.22\frac{\lambda}{D}

    Step-by-Step Solution

    See how the main results are calculated.

    1

    Step 1: Rayleigh Criterion

    Equation:

    θ=1.22λD\theta = 1.22\frac{\lambda}{D}

    Explanation:

    Minimum resolvable angular separation (radians).

    2

    Step 2: Values

    Result:

    λ=550nm,D=0.1mλ = 550 nm, D = 0.1 m
    3

    Step 3: Calculate θ

    Calculation:

    θ=1.22×5.5000e−70.1=6.7100e−6 rad\theta = 1.22\times\frac{5.5000e-7}{0.1} = 6.7100e-6\text{ rad}
    4

    Step 4: Arcseconds

    Result:

    θ ≈ 1.3840 arcsec
    5

    Step 5: Larger Aperture

    Bigger D → better (smaller θ) resolution.

    Explanation:

    Telescopes need large mirrors.

    6

    Step 6: Diffraction Limit

    Fundamental limit from wave nature of light.

    Explanation:

    Also applies to microscopes (NA).

    Frequently Asked Questions (FAQ)

    Why 1.22?

    First zero of Airy pattern for circular aperture.

    Atmospheric seeing?

    Ground telescopes often limited by turbulence, not diffraction.

    Practice MCQs

    1. Rayleigh criterion:
    2. Double aperture diameter:
    3. Longer wavelength:
    4. Unit of θ in formula:
    5. Resolution improves with:
    6. Eye resolution limited by:

    Related Calculators

    These tools connect to the same physics concepts used in this calculator.

    Thin Lens EquationFind image distance and magnification using 1/f = 1/u + 1/v.Spherical Mirror EquationCalculate image position and magnification for concave and convex mirrors.Lens PowerConvert focal length to diopters and combine thin lens powers.Critical AngleFind critical angle for total internal reflection between two media.Wave PropertiesCalculate wavelength, frequency, amplitude, and wave velocity.Related Waves topic.Error PropagationCombine measurement uncertainties for sums, products, quotients, and powers in experimental formulas.Related Measurement & Uncertainty topic.Quantum Harmonic OscillatorCalculate energy levels, wavefunctions, and quantum properties of harmonic oscillators.Related Modern Physics topic.