A light source whose surface is approximated by a circle with a radius of 3 cm is located 2 m from a screen. If an aperture with a 1-cm radius is placed between the source and the screen, how far from the screen can the aperture be placed without affecting the irradiance in the screen at the center of the patch of light passed by the aperture? If the aperture is moved twice as far from the screen, what will be the irradiance at the center of the patch as a fraction of the unobstructed irradiance?