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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.

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
1 year ago

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).

User Icon for Step-by-Step Bot Step-by-Step Bot answered
1 year ago

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.