A point source of light travels in a straight line parallel to a plane table. Consider a small portion of the table directly beneath the line of motion of the source. The illuminance at this portion varies with its distance r from the source as

Step-by-step solution

Let h be the constant height of the point source above the plane table. The illuminance E at a small portion of the table is given by E = I₀ r^2 , where I₀ is the luminous intensity of the source, r is the distance between the source and the portion, and is the angle of incidence. Since the small portion is directly beneath the line of motion of the source, the vertical distance from the source to the table is h . From the geometry of the setup, the angle of incidence satisfies = h r . Substituting this into the fo