Q: A radio antenna broadcasts a 1.0 MHz radio wave with 25 kW of power. What is the intensity of the wave at a distance of 30 km from the antenna?

$$2.2 \times 10$$^{-6}$$ \ \text{W/m}^2$$

Q: A laser beam passes through two polarizers, each oriented at $$30^\circ to $$the previous polarization direction. What fraction of the original intensity is transmitted?

$$\cos^2$ 30^\circ \times \cos^2$ 30^\circ$$

Question 1

A radio antenna broadcasts a 1.0 MHz radio wave with 25 kW of power. What is the intensity of the wave at a distance of 30 km from the antenna?

Accepted Answer

$$2.2 	imes 10$$^{-6}$$ \ 	ext{W/m}^2$$

Question 2

Given the intensity $$I = 2.2 	imes 10$$^{-6}$$ \ 	ext{W/m}^2 at 30 km $$from a radio antenna, what is the electric field amplitude $$E_0 at $$this distance? (Use $$c = 3.0 	imes 10^8$ \ 	ext{m/s}$$ and $$\$$epsilon_0$$ = 8.85 	imes 10$$^{-12}$$ \ 	ext{C}^2/(	ext{N} \cdot 	ext{m}^2))$$

Accepted Answer

$$E_0 = 0.041$$ \ 	ext{V/m}$$

Question 3

A polarized electromagnetic wave with intensity $$10 \ 	ext{W/m}^2$$ passes through a polarizing filter whose axis is at $$45^\circ to $$the plane of polarization. What is the transmitted intensity?

Accepted Answer

$$5.0 \ 	ext{W/m}^2$$

Question 4

According to Malus’s law, what is the intensity of light transmitted through a polarizer if the incident light is polarized and the angle between the light’s polarization and the polarizer’s axis is $$	heta$$?

Accepted Answer

$$I = I_0$ \cos^2$ 	heta$$

Question 5

A 50 mW laser beam polarized horizontally passes through two polarizers. The first is at $$30^\circ$$ from the horizontal, the second at $$60^\circ$$ from the horizontal. What is the power of the transmitted beam?

Accepted Answer

$$28 \ 	ext{mW}$$

Question 6

If a polarized light of intensity $$10 \ 	ext{W/m}^2$$ passes through a polarizing filter at $$60^\circ to $$the plane of polarization, what is the transmitted intensity?

Accepted Answer

$$2.5 \ 	ext{W/m}^2$$

Question 7

Three laser beams have wavelengths $$\$$lambda_1$$ = 400 \ 	ext{nm}$$, $$\$$lambda_2$$ = 600 \ 	ext{nm}$$, and $$\$$lambda_3$$ = 800 \ 	ext{nm}$$, each with power 1 W. Rank the photon energies $$E_1$$, $$E_2$$, and $$E_3$$ from largest to smallest.

Accepted Answer

$$E_1$$ \u003e $$E_2$$ \u003e $$E_3$$

Question 8

For the same three laser beams ($$\$$lambda_1$$ = 400 \ 	ext{nm}$$, $$\$$lambda_2$$ = 600 \ 	ext{nm}$$, $$\$$lambda_3$$ = 800 \ 	ext{nm}$$, each 1 W), rank the number of photons per second $$N_1$$, $$N_2$$, and $$N_3$$ delivered by the beams from largest to smallest.

Accepted Answer

$$N_3$$ \u003e $$N_2$$ \u003e $$N_1$$

Question 9

A radio wave is emitted uniformly in all directions from a point source. Which equation correctly describes the intensity $$I at a $$distance $$r$$ from the source with power $$P$$?

Accepted Answer

$$I = \frac{P}{4 \pi r^2$}$$

Question 10

A laser beam of wavelength $$600 \ 	ext{nm}$$ and power $$1 \ 	ext{W}$$ delivers photons at a rate $$N. $$What is the correct expression for $$N$$?

Accepted Answer

$$N = \frac{P \lambda}{hc}$$

Question 11

A polarized light beam passes through a polarizer whose axis is perpendicular ($$90^\circ) to $$the plane of polarization. What is the transmitted intensity?

Accepted Answer

$$0 \ 	ext{W/m}^2$$

Question 12

A radio wave has an electric field amplitude $$E_0$$ and intensity $$I. $$Which equation relates $$I$$ and $$E_0$$ for an electromagnetic wave in vacuum?

Accepted Answer

$$I = \frac{1}{2} c \$$epsilon_0$$ E_0$^2$$

Question 13

A laser beam of power $$P$$ and wavelength $$\lambda$$ delivers photons of energy $$E. $$Which equation gives the energy of a single photon?

Accepted Answer

$$E = \frac{hc}{\lambda}$$

Question 14

A horizontally polarized laser beam passes through a polarizer at $$0^\circ to $$the horizontal. What is the transmitted intensity?

Accepted Answer

$$10 \ 	ext{W/m}^2$$

Question 15

A laser beam passes through two polarizers, each oriented at $$30^\circ to $$the previous polarization direction. What fraction of the original intensity is transmitted?

Accepted Answer

$$\cos^2$ 30^\circ 	imes \cos^2$ 30^\circ$$

Question 16

Which of the following best explains why more photons are needed per second to deliver the same power for longer wavelength laser beams?

Accepted Answer

Longer wavelength photons have less energy, so more are needed to deliver the same power.

Question 17

A radio wave with intensity $$I$$ and electric field amplitude $$E_0 is $$detected. If the intensity increases by a factor of 4, by what factor does $$E_0$$ increase?

Accepted Answer

$$E_0$$ increases by a factor of 2.

Question 18

A laser beam of power $$P$$ and wavelength $$\lambda$$ delivers $$N$$ photons per second. If the wavelength is doubled, what happens to $$N ($$assuming $$P is $$constant)?

Accepted Answer

$$N$$ doubles.

Electromagnetic Waves, Polarization, and Photons – Step-by-Step Study Guidance

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