How much will the brightness appear to increase when a 60-watt bulb is moved from three feet to one foot from the page?

When assessing how brightness changes with distance, we use the inverse square law of light. This principle states that the intensity of light (or brightness) from a point source is inversely proportional to the square of the distance from the source.

In this scenario, when the 60-watt bulb is moved from three feet to one foot, we can apply the inverse square law. At three feet away, the intensity of light can be represented as I₁, and at one foot away, it can be represented as I₂. According to the law, the relationship can be defined as:

I ∝ 1/d²

So, at three feet (d = 3), we have:

I₁ ∝ 1/(3²) = 1/9

When the bulb is moved to one foot (d = 1):

I₂ ∝ 1/(1²) = 1

To find how much brighter it is when moving from three feet to one foot, we compare I₂ to I₁:

I₂/I₁ = (1) / (1/9) = 9

This means the brightness increases by a factor of nine times when the bulb is moved closer from three feet to