Calculating Intensity of 13-Watt Bulb at 1.2m Distance

[looi76]

Homework Statement

A low energy, 13-watt bulb illuminates your desk from a distance of 1.2m. You can assume that it acts as a point source and that it is 100% efficient. What is the intensity (power per unit area) at the desk (in Wmˉ²)?

Homework Equations

Velocity = Frequency * Wavelength
Intensity is proportional to amplilude²

The Attempt at a Solution

I don't know how to start!

 

[Doc Al]

Imagine the bulb as a point source sending out its energy equally in all directions. By the time the light has traveled 1.2 m, over how large an area is the total power spread? Hint: What's the area of a sphere of that radius?

 

[Moetasim]

I would approach this problem by using the equation for intensity, which is power per unit area. In this case, we are given the power of the bulb (13 watts) and the distance from the bulb to the desk (1.2m). We can use the inverse square law to calculate the intensity at the desk.

The inverse square law states that the intensity of a point source is inversely proportional to the square of the distance from the source. This means that as the distance increases, the intensity decreases by a factor of the square of the distance.

So, to calculate the intensity at the desk, we can use the formula:

Intensity = Power / (4πr²)

Where r is the distance from the source (in this case, 1.2m).

Plugging in the values, we get:

Intensity = 13 watts / (4π * (1.2m)²) = 2.22 Wmˉ²

Therefore, the intensity of the 13-watt bulb at a distance of 1.2m is 2.22 Wmˉ².