Margrt attaches a light bulb to the ceiling to illuminate a picture hanging on the wall d meters below the ceiling. Find at what distance x from the wall gives maximum light when the law

i. illumination decreases in inverse proportion to the second square of the distance f from the light source, and

ii. illumination of a surface is directly proportional to cos when is the angle between the light beam and the vector across the surface (Lambert's law),

are kept in mind.