A 100 watt bulb emits light in all directions. The distance R from the bulb is equal to 1.0 meter.
Complete the table below with calculated values of intensity of the bulb.
Distance from Source Intensity (W/m2)
R ?
2R ?
3R ?
c) If the bulb was replaced by a 75 watt bulb, at position 2R the intensity would be?
this is really nonsense. 100 watt light bulbs do not radiate 100 watts of luminous energy. So using the inverse square law is silly, at best.
To calculate the intensity of the light emitted by a 100 watt bulb at different distances, we need to use the inverse square law for light. The inverse square law states that the intensity of light decreases with the square of the distance from the source.
Mathematically, the formula for the intensity is:
Intensity = (Power / (4 * π * distance^2))
Where:
- Intensity is measured in watts per square meter (W/m^2)
- Power is the power of the light source, measured in watts (W)
- Distance is the distance from the source, measured in meters (m)
- π is a mathematical constant, approximately 3.14159
Now, let's calculate the intensity of the 100 watt bulb at different distances:
Distance from Source (R) Intensity (W/m^2)
1R (1.0 m) 100 / (4 * π * (1.0)^2)
2R (2.0 m) 100 / (4 * π * (2.0)^2)
3R (3.0 m) 100 / (4 * π * (3.0)^2)
Now we can perform the calculations:
Distance from Source (R) Intensity (W/m^2)
1R (1.0 m) 25.33 W/m^2 (rounded to two decimal places)
2R (2.0 m) 6.33 W/m^2 (rounded to two decimal places)
3R (3.0 m) 2.81 W/m^2 (rounded to two decimal places)
Next, we need to calculate the intensity at position 2R (2.0 m) for a 75 watt bulb. We can use the same formula as before, but with the new power value:
Intensity = (Power / (4 * π * distance^2))
Plugging in the values:
Intensity = (75 / (4 * π * (2.0)^2)
Calculating:
Intensity = 75 / 50.27
Intensity = 1.49 W/m^2 (rounded to two decimal places)
So, if the bulb was replaced by a 75 watt bulb, the intensity at position 2R (2.0 m) would be approximately 1.49 watts per square meter (W/m^2).