Question

What is the relationship between intensity and distance from a point source? Why should this be the cast? (Hint: think of the point source as being at the center of the sphere. How are the area of this sphere and the intensity of light related? It might help you to realize that no matter how far away you are the toal power output from the point source is the same. In other words, if you enclose a 50W light bulb in a sphere of radius R, the 50 W mst pass through the sphere no matter how large you make R.)

Answer 1

The intensity is given by the power per unit area. Thus if the source is considered a point source with Power output as P₀ .Then at a distance R from the source if we draw a sphere with the origin as the source and radius R the intensity i.e. the Power per unit area on this imaginary sphere would be

As 4*pi*R² is the area of the sphere. Thus no matter how large the sphere, it is considered that the entire Power output passes through the surface area of the sphere. But the Intensity that is power per unit area decreases with distance as defined by the equation.