The intensity of I of light from a light bulb, measured in watts per square meter (w/m^2), varies inversely as the square of the distance d from the light bulb. Suppose I is 85 w/m^2 when the distance is 5m. Find the intensity when the distance from the light bulb is 2m away.
I= ___ w/m^2
(simplify your answer. Type an integer,fraction, or mixed number.)
since I = k/d^2, I*d^2 = k, a constant. So, just set it up:
85*5^2 = I*2^2
Now just solve for I.
Well, distances can be a bit touchy. It's like when you're far away from a party and you're not really feeling the energy, but as you get closer, the intensity increases and you can't help but join in the fun!
Now, in this case, we have an inverse relationship going on. So, if the intensity of the light is inversely proportional to the square of the distance, we can set up a proportion to solve for the unknown intensity when the distance is 2m.
We know that I (intensity) is 85 w/m^2 when the distance is 5m, so this gives us the first part of the equation: I1 = 85 w/m^2 and d1 = 5m.
Now, we need to find the unknown intensity I2 when the distance is 2m, so d2 = 2m.
Using the inverse relationship, we can set up the proportion:
I1/d1^2 = I2/d2^2
Plugging in the values we know:
85/5^2 = I2/2^2
85/25 = I2/4
Cross multiplying, we get:
25 * I2 = 85 * 4
25 * I2 = 340
Dividing both sides by 25, we find:
I2 = 13.6 w/m^2
So, when the distance from the light bulb is 2m away, the intensity is approximately 13.6 w/m^2.
But remember, don't get too close to the light bulb or you might feel like a roasted marshmallow!
To find the intensity when the distance from the light bulb is 2m away, we can use the inverse square law.
The inverse square law states that the intensity of light is inversely proportional to the square of the distance from the source.
We are given that the intensity (I) is 85 w/m^2 when the distance (d) is 5m.
Using this information, we can set up the equation:
I = k/d^2
where k is the constant of proportionality.
To find the value of k, we can substitute the given values into the equation:
85 = k/5^2
Simplifying the equation:
85 = k/25
Multiplying both sides by 25:
k = 85 * 25
k = 2125
Now, we can use the value of k to find the intensity when the distance is 2m:
I = 2125 / 2^2
I = 2125 / 4
I = 531.25 w/m^2
Therefore, the intensity when the distance from the light bulb is 2m away is 531.25 w/m^2.
To find the intensity of light when the distance from the light bulb is 2m away, we can use the inverse square law formula:
I1 * d1^2 = I2 * d2^2
where I1 and d1 are the initial intensity and distance, and I2 and d2 are the final intensity and distance.
Given that I1 = 85 w/m^2 when d1 = 5m, we can substitute these values into the formula:
85 * (5^2) = I2 * (2^2)
Simplifying the equation, we have:
85 * 25 = I2 * 4
2125 = 4I2
To find I2, divide both sides of the equation by 4:
I2 = 2125 / 4
I2 ≈ 531.25 w/m^2
Therefore, the intensity of light when the distance from the light bulb is 2m away is approximately 531.25 w/m^2.