The minimum angular resolution (limit of resolution) for a circular aperture of diameter $a$ is given by:
where $\theta$ is the minimum angle that can be resolved, $\lambda$ is the wavelength, and $a$ is the aperture diameter.
Rayleigh's Criterion states that two point sources are just resolved when the central maximum of the diffraction pattern of one source falls on the first minimum of the other. For a circular aperture of diameter $a$, the angular limit of resolution is:
$\theta_{min} = \dfrac{1.22\lambda}{a}$
Resolving power is defined as $1/\theta_{min}$. A larger aperture gives a smaller $\theta_{min}$, meaning it can resolve finer details — this is why larger telescopes see more detail.
Why 1.22? For a circular aperture (unlike a slit), the first diffraction minimum occurs at $\sin\theta = 1.22\lambda/a$. The factor 1.22 comes from the first zero of the Bessel function $J_1(x)$, which describes circular diffraction.
Practical significance: The Hubble Space Telescope has a 2.4m mirror and achieves $\theta \approx 0.05$ arcseconds. Ground-based telescopes are limited by atmospheric turbulence, not diffraction. Modern techniques like adaptive optics correct for atmospheric distortion.
$\theta_{min}=1.22\lambda/a$. For this problem: $a=1.22\times500\times10^{-9}/(3\times10^{-7})=2.033$ m. The factor 1.22 arises from circular aperture diffraction (Bessel function first zero).
Resolving power $= 1/\theta_{min} = a/(1.22\lambda)$. A larger diameter $a$ gives smaller minimum angle, so you can distinguish finer detail. This is why observatories use large mirrors.
Shorter wavelength → smaller diffraction limit → better resolution. UV telescopes can resolve finer detail than optical telescopes of the same aperture. Radio telescopes need enormous dishes because radio wavelengths are millions of times longer.
Always convert to SI first: $\lambda = 500$ nm $= 5\times10^{-7}$ m. Answer $2.033$ m $\times 100 = 203.3$ cm, nearest integer $= 203$ cm.