Worksheet: Radiative Power of Electromagnetic Radiation

In this worksheet, we will practice determining the radiant power received per unit area at a distance from a point source of electromagnetic radiation.

Q1:

A point source of electromagnetic radiation has a radiant power of 225 W. The radiation emitted by the source is all visible light, with wavelengths between 400 nm and 700 nm. Each wavelength emitted has a 1 nm difference in length to its most similar emitted wavelength. All the wavelengths are emitted with the same energy. How much radiant power is emitted at each wavelength?

Q2:

Three point sources of electromagnetic radiation are at different points on the surface of a sphere centered on the point 𝑂 , as shown in the diagram. The radius of the sphere is 2.5 m. What is the irradiance at the point 𝑂 ?

Q3:

An object that emits electromagnetic radiation uniformly is at the position 𝑂 , as shown in the diagram. Which of the following statements most correctly describes how the irradiance 𝐼 produced by the radiating object at the points 𝑃 , 𝑃 , and 𝑃 on the surface of a sphere centered at 𝑂 compare to each other?

  • A 𝐼 > 𝐼 > 𝐼
  • B 𝐼 = 𝐼 = 𝐼
  • C 𝐼 > 𝐼 = 𝐼
  • D 𝐼 = 𝐼 > 𝐼
  • E 𝐼 > 𝐼 > 𝐼

Q4:

A point source emits electromagnetic radiation with a radiant power of 150 W. What is the irradiance at a point 2.4 m from the source?

Q5:

Which of the following formulas correctly relates the irradiance 𝐼 of electromagnetic radiation at a point to the distance 𝑑 from its source and the radiant power 𝑃 of the emitted electromagnetic radiation?

  • A 𝐼 = 𝑃 4 𝑑
  • B 𝐼 = 𝑃 4 𝜋 𝑑
  • C 𝐼 = 𝑃 𝑑
  • D 𝐼 = 𝑃 4 𝜋 𝑑
  • E 𝐼 = 4 𝜋 𝑃 𝑑

Q6:

A point source emits electromagnetic radiation. The irradiance at a point 3.43 m from the source is 1.75 W/m2. What radiant power does the source emit?

Q7:

Calculate the total irradiance 𝐼 at the point shown in the diagram due to the point sources of electromagnetic radiation.

Q8:

At a point 𝑃 , the irradiance 𝐼 due to the electromagnetic radiation emitted from a point source equals 𝐼 × 1 0 , where 𝐼 is the irradiance due to the same source at a point 𝑃 that is 15 cm from the source. How far from the source is 𝑃 ?

Q9:

A point source emits electromagnetic radiation with a radiant power of 655 W. The irradiance at another point is 8.25 W/m2. What is the distance of the point from the source?

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