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θ≈1.22 λD\theta \approx 1.22\,\frac{\lambda}{D}

Why this formula appears here

This reach is the approach’s defining strength and its defining limitation is spatial resolution, which is fixed by the physics of diffraction rather than by mission budget. For a telescope with aperture diameter D observing light of wavelength λ\lambda , the smallest angular separation it can resolve is approximately θ≈1.22 λD\theta \approx 1.22\,\frac{\lambda}{D}. This relation is why an exoplanet studied by transmission spectroscopy is a single point of light with no visible surface at all — the target subtends an angle far smaller than θ\theta for any existing telescope, so every observation is necessarily a disk-integrated average over the whole illuminated hemisphere. Even for solar-system bodies, where θ\theta is…

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θ\theta

Symbol θ

θ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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DD

Symbol D

D occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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With a fixed numerator, increasing a nonzero denominator reduces the fraction. Its accuracy depends on the assumptions and range of use described in the article.

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Published contexts (1)

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θ≈1.22 λD.\theta \approx 1.22\,\frac{\lambda}{D}.

Equation 3 · Space Science

Comparing the Main Approaches to Planetary Science and Exploration

This equation gives an approximation: it relates the quantities while allowing an approximation.

This reach is the approach’s defining strength and its defining limitation is spatial resolution, which is fixed by the physics of diffraction rather than by mission budget. For a telescope with aperture diameter D observing light of wavelength λ\lambda , the smallest angular separation it can resolve is approximately θ≈1.22 λD\theta \approx 1.22\,\frac{\lambda}{D}. This relation is why an exoplanet studied by transmission spectroscopy is a single point of light with no visible surface at all — the target subtends an angle far smaller than θ\theta for any existing telescope, so every observation is necessarily a disk-integrated average over the whole illuminated hemisphere. Even for solar-system bodies, where θ\theta is…

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