The Abbe sine condition is a criterion used in optics to determine the conditions for achieving sharp imaging in optical systems, such as microscopes. It states that for a point source of light to be imaged clearly, the sine of the angle of light rays entering the optical system must be proportional to the sine of the angle of light rays exiting the system. This relationship ensures that the light rays converge properly to form a clear image. This condition is particularly important in the design of lenses and microscopes, as it helps in minimizing optical aberrations. When the numerical aperture of the optical system is maximized, the Abbe sine condition is satisfied, leading to improved resolution and clarity in the resulting images.