The illumination (L) received by an object varies inversely as the square of the

distance (d) of the object from the source of light.

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To find the equation that represents the relationship between the illumination (L) and the distance (d) of the object from the source of light, we can use the concept of inverse variation.

Inverse variation states that if two variables are inversely proportional, their product remains constant. In this case, the product of the illumination and the square of the distance should remain constant.

Mathematically, this can be represented as:

L * d^2 = k

Where:
L = Illumination received by the object
d = Distance of the object from the source of light
k = Constant of variation

To solve for the constant of variation (k), we need to use a specific illumination and distance value from the problem.

For example, let's say the object receives an illumination of 10 units when it is 5 meters away from the source of light. We can substitute these values into the equation:

10 * (5)^2 = k
10 * 25 = k
k = 250

Now, we have the equation:

L * d^2 = 250

This equation represents the inverse variation relationship between the illumination (L) and the distance (d) of the object from the source of light.

L = k/d^2