## Answers

The equation needed is:

Where *P* is the power of light emitted at the filament and *d* is the distance from filament to the surface of the bulb.

#### Explanation:

First some assumptions:

1. The bulb is a filament bulb.

2. The filament is a point source of light.

The first assumption means that the light travels a distance from filament to the surface of the bulb. The second means that the light spreads out across a sphere.

Define variables:

The distance from filament to the surface of the bulb is *d*. The electrical power converted to light at the filament is *P*.

The intensity of light at the surface of the bulb is *I*.

As light travels from a source it spreads out to cover an area, *A*, at a given distance. In this case the source is a point source and the light spreads out in all directions to fill a sphere. So if the light has travelled distance *d* the radius of the sphere is *d*. All light that was emitted at the filament and travelled distance *d* will cover the surface area of a sphere of radius *d*.

The equation for light intensity is:

As we have seen above the relevant area for this case is the surface are of a sphere radius *d*:

So now combine the equations to get an equation for the light intensity at the surface of the bulb: