The intensity of light (L) from a given source is inversely proportional to the square of the distance (D) from it. At a distance of 25 m, a light has an intensity of 64 candelas (CD). Find the intensity of light at a point 20 m from the source.
Let I represent the intensity of light at a point 20 m from the source.
According to the given information, intensity (L) is inversely proportional to the square of the distance (D) from the source. This can be written as:
L = k/D^2
where k is a constant.
We can use the given information to find the value of k. At a distance of 25 m, the light has an intensity of 64 candelas (CD):
64 = k/25^2
Simplifying:
64 = k/625
k = 64 * 625
k = 40000
Now we can use this value of k to find the intensity at a point 20 m from the source:
I = 40000/20^2
I = 40000/400
I = 100 CD
Therefore, the intensity of light at a point 20 m from the source is 100 candelas (CD).
According to the given information, the intensity of light (L) is inversely proportional to the square of the distance (D). This can be represented by the equation:
L ∝ 1/D^2
We can express this relationship using a proportionality constant (k) as:
L = k/D^2
To find the value of k, we can use the given information. At a distance of 25 m, the light has an intensity of 64 candelas (CD):
64 = k/25^2
64 = k/625
To find the value of k, we can cross-multiply:
k = 64 * 625
k = 40,000
Now we can use this value of k to find the intensity of light at a point 20 m from the source:
L = 40,000/20^2
L = 40,000/400
L = 100 candelas (CD)
Therefore, the intensity of light at a distance of 20 m from the source is 100 candelas.