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The area of illumination increases four times when the distance between the light source and the illuminated area is _____.

  1. doubled

  2. quadrupled

  3. tripled

  4. halved

The correct answer is: doubled

The correct choice is based on the relationship between distance from a light source and the area it illuminates, which is governed by the inverse square law. According to this principle, the illumination intensity decreases with the square of the distance from the source. When the distance from the light source is doubled, the area covered by light increases by a factor of four. This is because the area of illumination is proportional to the square of the distance. As such, if the distance doubles, the area illuminated becomes four times larger (2 squared equals 4). Understanding this concept is crucial in fields such as lighting design and architectural planning, where knowing how distance affects illumination can help in creating effective light arrangements. The other options either suggest an incorrect relationship or do not align with the mathematical principles governing light distribution.