I apologize for any confusion. The equation you provided, r = 0.61λ/NA, represents the Rayleigh criterion for the resolution of an optical system. In this equation, r represents the minimum resolvable distance, λ is the wavelength of light used, and NA refers to the numerical aperture of the optical system.
You are correct that in general, lower wavelengths of light provide higher resolution. As the wavelength decreases, the ability to distinguish fine details improves. However, the equation itself does not imply that resolution increases with lower wavelength.
The equation determines the minimum resolvable distance based on the wavelength and the numerical aperture of the optical system. A smaller minimum resolvable distance (smaller r) indicates a higher resolution, as it means the system can distinguish smaller details.
The numerical aperture (NA) of an optical system is a measure of its ability to gather and focus light. It depends on factors such as the refractive index of the medium and the angle at which the light enters the system. The larger the numerical aperture, the greater the resolution potential of the optical system.
So, in summary, the equation allows you to calculate the minimum resolvable distance (r) based on the wavelength (λ) and the numerical aperture (NA) of the optical system. It does not directly indicate that resolution increases with lower wavelength, but lower wavelengths, in general, provide higher resolution.