A light bulb hangs from a ceiling at height h metres above the floor, directly above point N. At any point A on the floor which is x metres from the light bulb, the illumination I is given by I = (squareroot(8)cos(theta))/x² units.

a. If NA = 1 metre, show that at A, I = squareroot(8)cos(theta)sin²(theta)

b. The light bulb may be lifted or lowered to change the intensity at A. Assuming NA=1 metre, find the height the bulb should be above the floor for greatest illumination at A.

A light bulb hangs from the ceiling at height h metres above the floor, directly above point N. At any point A on the floor which ceiling is x metres from the light bulb, the illumination / is given by L & light bulb I = V8 cos units. H a If NA = 1 metre, show that at A, I = V8 cos 0 sin20. h b The light bulb may be lifted or lowered to change the intensity at A. Assuming NA = 1 metre, find the height the bulb should be above the floor for greatest illumination floor at A. N A