if i0i0i_0 = 20.0 w/m2w/m2 , θ0θ0theta_0 = 25.0 degreesdegrees , and θtaθtatheta_ta = 40.0 degreesdegrees , what is the transmitted intensity i1i1i_1 ? Express your answer numerically in watts per square meter.

Answers

Answer 1

The transmitted intensity i1 is approximately 19.32 watts per square meter.

An indicator of a physical phenomenon's strength or power, such as light, sound, or radiation, is its intensity. It is often expressed in terms of the quantity of energy being transmitted or received per unit area or volume. For instance, the intensity of light is expressed in watts per square metre, while the strength of sound is expressed in watts per square metre per hertz. Distance, direction, and the qualities of the medium through which the phenomenon is transmitted can all have an impact on intensity.

To find the transmitted intensity (i1), we need to use the formula:

[tex]i1 = i0 * cos(θ0 - θta)[/tex]

where i0 is the initial intensity, [tex]θ0[/tex]is the initial angle, and [tex]θta[/tex] is the transmitted angle.

Step 1: Calculate the difference between the angles:
[tex]Δθ = θ0 - θta[/tex] = 25.0 degrees - 40.0 degrees = -15.0 degrees

Step 2: Convert the angle difference to radians:
[tex]Δθ[/tex](in radians) = -15.0 degrees *[tex](\pi /180)[/tex] ≈ -0.2618 radians

Step 3: Calculate the cosine of the angle difference:
[tex]cos(Δθ) ≈ cos(-0.2618)[/tex]≈ 0.9659

Step 4: Calculate the transmitted intensity (i1):
i1 = i0 * [tex]cos(Δθ)[/tex] = 20.0[tex]W/m^2[/tex] * 0.9659 ≈ 19.32 [tex]W/m^2[/tex]

So, the transmitted intensity i1 is approximately 19.32 watts per square meter.


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