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gogolik [260]
3 years ago
11

Many physical quantities are connected by inverse square laws, that is, by power functions of the form f(x)=kx^(-2). In particul

ar, the illumination of an object by a light source is inversely proportional to the square of the distance from the source. Suppose that after dark you are in a room with just one lamp and you are trying to read a book. The light is too dim and so you move halfway to the lamp. How much brighter is the light?
Physics
1 answer:
goldenfox [79]3 years ago
3 0

Answer:

  • 4 times

Explanation:

Since the equation for the illumination of an object, i.e. the brightness of the light, is <em>inversely proportional to the square of the distance from the light source</em>, the form of the function is:

  • f(x) = k.x⁻²

Where x is the distance between the object and the light force, k is the constant of proportionality, and f(x) is the brightness.

Then, if you move halfway to the lamp the new distance is x/2 and the new brightness (call if F) is :

F=k(x/2)^{-2}=\frac{k}{(x/2)^2}= \frac{k}{x^2}. 4=f(x).4

Then, you have found that the light is 4 times as bright as it originally was.

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