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 π‘ƒοŠ§, π‘ƒοŠ¨, and π‘ƒοŠ© on the surface of a sphere centered at 𝑂 compare to each other?

  • A𝐼>𝐼>𝐼
  • B𝐼=𝐼>𝐼
  • C𝐼=𝐼=𝐼
  • D𝐼>𝐼=πΌο…οŒ―οŒ―οŒ―οŽ‘οŽ οŽ’
  • E𝐼>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?

  • A𝐼=𝑃4πœ‹π‘‘
  • B𝐼=𝑃4𝑑
  • C𝐼=π‘ƒπ‘‘οŠ¨
  • D𝐼=𝑃4πœ‹π‘‘οŠ¨
  • E𝐼=4πœ‹π‘ƒπ‘‘οŠ¨

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 π‘ƒοŠ§, the irradiance 𝐼 due to the electromagnetic radiation emitted from a point source equals 𝐼×10, where 𝐼 is the irradiance due to the same source at a point π‘ƒοŠ¨ that is 15 cm from the source. How far from the source is π‘ƒοŠ§?

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?

Q10:

The graph shows the change in the spectral irradiance incident at a surface with the wavelength of the incident electromagnetic radiation. What is the ratio of the total energy of the electromagnetic radiation that has wavelengths less than 500 nm to the total energy of the electromagnetic radiation that has wavelengths of 500 nm or greater?

Q11:

The irradiance of sunlight at a point on Earth’s surface is 1,360 W/m2 and the irradiance of moonlight at the same point is 20 mW/m2. Assuming that the distance from the point to the Sun is 149.6Γ—10 km, that the distance from the point to the Moon is 384.4Γ—10 km, and that the light from the Moon is only due to reflected light from the Sun, find the ratio of the radiant power of sunlight reflected from the Moon to the Sun’s radiant power output.

  • A4.2Γ—10
  • B4.9Γ—10
  • C7.1Γ—10
  • D9.7Γ—10
  • E5.6Γ—10

Q12:

Two point sources of electromagnetic radiation are at different distances from a point 𝑃 at which the total irradiance due to the sources is 4.0 W/m2. One of the sources emits electromagnetic radiation with a radiant power of 25 W. The irradiance at 𝑃 due to this source is 0.75 of the total irradiance at 𝑃. The radiant power of the other source is unknown, but its distance from 𝑃 is known to be 2.15 m.

What is the distance from the 25 W point source to the point 𝑃?

  • A6.2 m
  • B1.7 m
  • C0.81 m
  • D7.0 m
  • E3.3 m

What is the radiant power of the point source 2.15 m from the point 𝑃?

  • A26 W
  • B83 W
  • C58 W
  • D41 W
  • E65 W

Q13:

Three point sources of electromagnetic radiation are at different points on the surface of a 7.2 m radius sphere, as shown in the diagram. The points where irradiance is measured are both at points above or below the 𝑦-axis in the 𝑦𝑧-plane. The shortest distance along the 𝑦-axis from the sphere’s surface to the point at which the irradiance equals 𝐼 is 62 cm. The 333 W source is on the 𝑧-axis with no displacement in the π‘₯-direction or the 𝑦-direction.

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

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

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