Question

Why does the brightness of the light emitted by a flashlight decrease as the flashlight moves farther away from you?

Answer 1

Due to inverse square law followed by light.

Explanation:

Let a light source of intensity `I_o` be placed at the center of a sphere of radius `r`. The light travels and spreads equally in all directions.
The surface area of the sphere is given by the expression `4pi r^2`.
As such the intensity of light at a distance equal to the radius of the sphere is given by
`I_r=`Initial Intensity`/`Area of spread`=I_o/(4pir^2)`
`I_r prop 1/r^2`

It is seen from this expression that intensity is inversely proportional to the square of the distance. As we move away from the light source the intensity decreases at the rate of square of the distance from the source.

Brightness being the perception of intensity, i.e., more the intensity more bright the object is perceived and vice versa.