Exam 25: Electromagnetic Waves

A laser beam takes 24 ms to travel from a rocket to the reflective surface of a planet and back to the rocket.How far is the rocket from this planet's surface? (c = 3.0 × 10⁸ m/s)

Unpolarized light is incident upon two ideal polarizing filters that do not have their transmission axes aligned.If $19 \%$ of the light passes through this combination,what is the angle between the transmission axes of the two filters?

As shown in the figure,the orientation of the transmission axis for each of three ideal polarizing sheets is labeled relative to the vertical direction.A beam of light,polarized in the vertical direction,is incident on the first polarizer with an intensity of 1.00 kW/m².What is the intensity of the beam after it has passed through the three polarizing sheets when θ₁ = 30°,θ₂ = 30°,and θ₃= 60°?

What is Brewster's angle for light traveling in vacuum and reflecting off a piece of glass having a refractive index of 1.52?

The rate of energy flow per unit area of an electromagnetic wave has an average value of 0.695 W/m².The wave is incident at right angles upon a rectangular area measuring 1.5 m by 2.0 m.How much total energy falls upon this rectangle each minute? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²,μ₀ = 4π × 10^-7 T ∙ m/A,c = 3.0 × 10⁸ m/s)

A sinusoidal electromagnetic wave is propagating in vacuum.At a given point and at a particular time the $\vec { E }$ field is in the +x direction and the $\vec { B }$ field is in the -y direction,and at that point the intensity of the wave is $0.45 \mathrm {~W} / \mathrm { m } ^ { 2 }$ $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , \right.$ $\mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } ,$ $\left. \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \mathrm { C } ^ { 2 } / \mathrm { N } \cdot \mathrm { m } ^ { 2 } \right)$ (a)What is the direction of propagation of the wave? (b)What is the $\vec { E }$ field amplitude at the given point?

A beam of light is polarized in a vertical plane and has an intensity I₀.The beam passes through an ideal polarizer and then through an ideal analyzer whose axis is set horizontally.If the axis of the polarizer is set at 60° with the vertical,what is the ratio of the intensity of the final beam to I₀?

A radiometer has two square vanes (1.0 cm by 1.0 cm),attached to a light horizontal cross arm,and pivoted about a vertical axis through the center,as shown in the figure.The center of each vane is 6.0 cm from the axis.One vane is silvered and it reflects all radiant energy that falls upon it.The other vane is blackened and it absorbs all incident radiant energy.Radiant energy,having an intensity of 300 W/m²,is incident normally upon the front surfaces of both vanes.What is the radiant power absorbed by the blackened vane?

A light source radiates 60.0 W of single-wavelength sinusoidal light uniformly in all directions.What is the amplitude of the $\vec { B }$ field of this light at a distance of 0.700 m from the bulb?(ε₀ = 8.85 × 10^-12 C²/N ∙ m²,μ₀ = 4π × 10^-7 T ∙ m/A,c = 3.0 × 10⁸ m/s)

An 800-kHz sinusoidal radio signal is detected at a point 6.6 km from the transmitter tower.The $\vec { E }$ field amplitude of the signal at that point is 0.780 V/m.Assume that the signal power is radiated uniformly in all directions and that radio waves incident upon the ground are completely absorbed.What is the amplitude of the $\vec { B }$ field of the signal at that point? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²,c = 3.0 × 10⁸ m/s,μ₀ = 4π × 10^-7 T ∙ m/A)

How much time does it take a beam of light to travel 2.9 km through space.(c = 3.0 × 10⁸ m/s)

In an electromagnetic wave in free space,the $\vec { E }$ field and $\vec { B }$ fields are

Polarized light of intensity S₀ passes through an ideal polarizer.If the E vector of the polarized light is horizontal what,in terms of the initial intensity S₀,is the intensity of the light that passes through a polarizer if that polarizer is tilted $0.449 \mathrm { rad }$ from the horizontal?

When unpolarized light from air (with refractive index 1.00)strikes a piece of glass with index of refraction 1.80,the reflected light is found to be completely polarized when the angle of incidence is equal to Brewster's angle.What is the angle of refraction in this case?

An 800-kHz radio signal is detected at a point 9.5 km distant from a transmitter tower.The $\vec { E }$ field amplitude of the signal at that point is 0.23 V/m.Assume that the signal power is radiated uniformly in all directions and that radio waves incident upon the ground are completely absorbed.What is the average electromagnetic energy density at that point? (c = 3.0 × 10⁸ m/s,μ₀ = 4π × 10^-7 T ∙ m/A,ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A 2.4 x $10^{14}$ Hz laser emits a 3.5-μs pulse that is 5.0 mm in diameter.The average energy density in the beam is $0.65 \mathrm {~J} / \mathrm { m } ^ { 3 }$ What average power is emitted by this laser? (c = 3.0 × 10⁸ m/s,μ₀ = 4π × 10^-7 T ∙ m/A,ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

How far does a beam of light travel through space in one 365-day year? (c = 3.0 × 10⁸ m/s)

A vertically polarized beam of light of intensity 100 W/m² passes through two ideal polarizers.The transmission axis of the first polarizer makes an angle of 20.0° with the vertical,and the transmission axis of the second one makes an angle of 40.0° with the vertical.What is the intensity of the light after it has passes through both polarizers?

If the magnetic field in a traveling electromagnetic wave has a maximum value of 16.5 nT,what is the maximum value of the $\vec { E }$ field associated with this wave? (c = 3.00 × 10⁸ m/s)

How far does light travel in 1.0 μs? (c = 3.0 × 10⁸ m/s)