Q: A remote control emits electromagnetic radiation at a frequency $$f = 1.0 \times 10$$^{14}$$\ \mathrm{Hz}. $$What is the wavelength $$\lambda of $$this radiation in vacuum?

$$\lambda = 3.0 \times 10$$^{-6}$$\ \mathrm{m}$$

Q: A laser emits a beam with electric field amplitude $$E_{max} = 2.76 \times 10^6$\ \mathrm{V/m}. $$What is the maximum magnetic field $$B_{max} in $$the beam?

$$B_{max} = 9.2 \times 10$$^{-3}$$\ \mathrm{T}$$

Q: Which law describes the relationship between the angles of incidence and refraction when light passes between two media with different indices of refraction?

Snell's Law: $$\frac{\sin \theta_a}{\sin \theta_b} = \frac{n_b}{n_a}$$

Q: If the index of refraction of a material is $$n = 1.5$$, what is the speed $$v of $$light in this material?

$$v = 2.0 \times 10^8$\ \mathrm{m/s}$$

Question 1

Which of the following statements best describes the difference between mechanical and electromagnetic waves?

Accepted Answer

Mechanical waves require a medium to travel, while electromagnetic waves can travel through a vacuum.

Question 2

A sinusoidal wave has a wavelength $$\lambda = 2\ \mathrm{m}$$ and a period $$T = 0.01\ \mathrm{s}. $$What is the speed $$v of $$the wave?

Accepted Answer

$$v = 200\ \mathrm{m/s}$$

Question 3

Which equation correctly relates the speed of light $$c$$, the permittivity of free space $$\$$epsilon_0$$, and the permeability of free space $$\$$mu_0$$?

Accepted Answer

$$c = \frac{1}{\sqrt{\$$epsilon_0$$ \mu_0$}}$$

Question 4

A remote control emits electromagnetic radiation at a frequency $$f = 1.0 	imes 10$$^{14}$$\ \mathrm{Hz}. $$What is the wavelength $$\lambda of $$this radiation in vacuum?

Accepted Answer

$$\lambda = 3.0 	imes 10$$^{-6}$$\ \mathrm{m}$$

Question 5

The electric field $$E$$ and magnetic field $$B in an $$electromagnetic wave are related by which equation?

Accepted Answer

$$E = cB$$

Question 6

A light ray passes from water ($$n_a = 1.33) $$into air ($$n_b = 1.00) at an $$incident angle of $$60^\circ. $$What is the angle of refraction $$	heta_b in $$air? (Use Snell's law.)

Accepted Answer

$$	heta_b = 83.0^\circ$$

Question 7

Which of the following best describes total internal reflection?

Accepted Answer

It occurs when light passes from a medium with higher index of refraction to one with lower index, and the incident angle exceeds the critical angle.

Question 8

The average energy density $$u_{avg} of an $$electromagnetic wave with maximum electric field $$E_{max} is $$given by:

Accepted Answer

$$u_{avg} = \frac{1}{2} \$$epsilon_0$$ E_{max}^2$$

Question 9

A beam of unpolarized light with intensity $$I_0$$ passes through two polarizing filters. The first filter is aligned vertically, and the second is at $$30^\circ to $$the first. What is the intensity $$I_2$$ after the second filter?

Accepted Answer

$$I_2$$ = \frac{1}{2} $$I_0$$ \$$cos^2 30$$^\circ$$

Question 10

Which of the following is NOT a property of electromagnetic waves in a vacuum?

Accepted Answer

They are always longitudinal.

Question 11

A laser emits a beam with electric field amplitude $$E_{max} = 2.76 	imes 10^6$\ \mathrm{V/m}. $$What is the maximum magnetic field $$B_{max} in $$the beam?

Accepted Answer

$$B_{max} = 9.2 	imes 10$$^{-3}$$\ \mathrm{T}$$

Question 12

Which law describes the relationship between the angles of incidence and refraction when light passes between two media with different indices of refraction?

Accepted Answer

Snell's Law: $$\frac{\sin 	heta_a}{\sin 	heta_b} = \frac{n_b}{n_a}$$

Question 13

If the index of refraction of a material is $$n = 1.5$$, what is the speed $$v of $$light in this material?

Accepted Answer

$$v = 2.0 	imes 10^8$\ \mathrm{m/s}$$

Question 14

Which phenomenon explains why a prism separates white light into its constituent colors?

Accepted Answer

Dispersion

Question 15

A wave is described by $$y(x, t) = A \sin(2\pi f t - kx). $$What does the parameter $$A$$ represent?

Accepted Answer

The amplitude of the wave

Question 16

Which of the following is a correct statement about the polarization of electromagnetic waves?

Accepted Answer

Polarizing filters transmit only the component of the electric field aligned with their axis.

Question 17

A ray of light is traveling in glass (index $$n_{glass}) $$immersed in water ($$n_{water} = 1.33). If $$the critical angle for total internal reflection is $$48.7^\circ$$, what is the index of refraction of the glass?

Accepted Answer

$$n_{glass} = 1.77$$

Question 18

Which region of the electromagnetic spectrum has the shortest wavelength?

Accepted Answer

Gamma rays

Question 19

If the intensity of unpolarized light after passing through a polarizer is $$I_1$$, what is the intensity after passing through a second polarizer at angle $$\phi to $$the first?

Accepted Answer

$$I_2$$ = $$I_1$$ \$$cos^2$$ \phi$$

Electromagnetic Waves: Properties, Behavior, and Applications

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