Intensity of EM radiation for two incoherent waves?

[vrobins1]

Homework Statement

Two incoherent EM waves of intensities 10I₀ and 14I₀ travel in the same direction in the same region of space. What is the intensity of EM radiation in this region?

Homework Equations

I = I₁+I₂ + 2√(I₁I₂) or
I = I₁+I₂ - 2√(I₁I₂)

The Attempt at a Solution

I tried using the above formula adding AND subtracting (using 10 and 14 as my I₁ and I₂), but keep getting the answer wrong. I'm not sure how to go about this problem even though it seems simple.
Can anyone offer any insight? Thanks.

 

[AvroArrow]

The answer is 24I0. The equation you used is correct, but the order of the I1 and I2 matters. In this case, I1 = 10I0 and I2 = 14I0, so the equation should be:I = I1 + I2 + 2√(I1I2) = 10I0 + 14I0 + 2√(10I0 * 14I0) = 24I0

 

[nlightner]

I would first clarify the term "incoherent" in this context. Incoherent waves refer to waves that have random phase differences and therefore do not exhibit constructive or destructive interference. This means that the intensities of the two waves cannot simply be added together.

To calculate the intensity of the resulting EM radiation, we need to use the formula for the sum of two incoherent waves, which is I = I1 + I2. In this case, the intensities of the two waves are 10I0 and 14I0, so the resulting intensity would be 24I0.

It is important to remember that the intensity of EM radiation is proportional to the square of the electric field amplitude, so the resulting electric field amplitude would be √(24I0).

In summary, the intensity of EM radiation in this region would be 24 times the initial intensity I0, and the resulting electric field amplitude would be √(24) times the initial electric field amplitude.