Question

If a light is moved twice (2x) as far from a surface, the area the light covers is ___ as big.

Answer 1

Answer:

The correct option is;

- 4x

Explanation:

From the inverse square law, as the distance from the source of a physical quantity increases, the intensity of the source is spread over an area proportional to the square of the distance of the object from the source

The inverse square law can be presented as follows;

$I = \dfrac{S}{4\times \pi \times r^2 }$

As the distance, r, increases, the surface it covers also increases by the power of 2

Therefore, where the distance increases from r to 2·r, we have;

When, I, remain constant

$I = \dfrac{4\times S}{4\times \pi \times (2\cdot r)^2 } = I = \dfrac{4\times S}{4\times 4\times \pi \times r^2 } = \dfrac{S}{4\times \pi \times r^2 }$

The surface increases to 4·S by the inverse square law

Therefore, the correct option is 4 × x.