Physics 202-Section 2G Worksheet 9-Electromagnetic Radiation and Polarizers

Formulas and Concepts  Electromagnetic (EM) waves are forms of energy that have magnetic and electric components. EM waves carry energy, not matter.  EM waves all travel at the speed of light, which is about 3*108 m/s. The speed of light is often represented by the letter c.  Only small part of the EM spectrum is visible to us (colors).  Waves are defined by their frequency (measured in hertz) and wavelength (measured in meters). These quantities are related to velocity of waves according to the formula: 풗 = 흀풇 and for EM waves: 풄 = 흀풇  Intensity is a property of EM waves. Intensity is defined as power per area. 푷 푺 = , where P is average power 푨 o Intensity is related the magnetic and electric fields associated with an EM wave. It can be calculated using the magnitude of the magnetic field or the electric field. o Additionally, both the average magnetic and average electric fields can be calculated from the intensity. ퟐ ퟐ 푩 푺 = 풄휺ퟎ푬 = 풄 흁ퟎ  Polarizability is a property of EM waves. o Unpolarized waves can oscillate in more than one orientation. Polarizing the wave (often light) decreases the intensity of the wave/light. o When unpolarized light goes through a polarizer, the intensity decreases by 50%. ퟏ 푺 = 푺 ퟏ ퟐ ퟎ o When light that is polarized in one direction travels through another polarizer, the intensity decreases again, according to the angle between the orientations of the two polarizers. ퟐ 푺ퟐ = 푺ퟏ풄풐풔 휽  this is called Malus’ Law.

1. A radio wave has a frequency of 1605 kHz. What is the wavelength of the radio wave?

186.92 m. Radio waves are electromagnetic waves, and therefore travel at the speed of light. Use the formula 풄 = 흀풇 plugging in 3*108 for c and 1605000 Hz for f (converting kilohertz to hertz). Divide to get 186.92. Wavelength is measured in meters.

2. The magnetic field emitted by a laser is 0.003 T.

a) What is the average intensity of the waves emitted by the laser?

ퟐ 2.15 *109 use the formula 푺 = 풄 푩 . Plug in 0.003 T for B, c is 3e8, and mu is the magnetic 흁ퟎ constant: 4(pi)e-7.

b) What is the magnitude of the average electric field emitted by the laser?

900,000 N/C. Take the intensity from the last question and use the formula that includes electric ퟐ field. 푺 = 풄휺ퟎ푬 . Substitute in 3e8 for c, 2.15e9 for S, and the permittivity of free space (a constant) for epsilon (8.85e-12). Solve for E.

3. Unpolarized light of intensity 2000 W/m2 passes through three polarizers (A, B, and C).

a) Polarizer A is oriented to the vertical. What is the intensity of the light after it passes through Polarizer A?

1000 W/m2. No matter the orientation, if UNPOLARIZED light travels through ANY polarizer, it’s intensity will be cut in half.

b) The light from Polarizer A proceeds to pass through Polarizer B. Polarizer B is oriented 18 degrees from the vertical. What is the intensity of the light exiting Polarizer B?

904.5 W/m2. Use Malus’ Law. S2 (the new intensity) = S1 (old intensity) * cos2(angle between 2 polarizers). S2 = 1000cos2(18°) = 904.5.

c) The light from Polarizer B proceeds to pass through Polarizer C. Polarizer C is oriented 44 degrees from the vertical. What is the intensity of the light exiting Polarizer C?

730.7 W/m2. Use Malus’ Law again. S1 is now the answer to the previous question (904.5), and the angle is the angle between the 44-degree polarizer and the 18-degree polarizer, which is 26 degrees. 904.5cos2(26) = 730.7.

4. Horizontally polarized light enters a polarizer and exits with an intensity of 12.8 W/m2. If the polarizer was oriented at 38 degrees from the horizontal, what was the intensity of the light incident on the polarizer?

20.6 W/m2. Rearrange Malus’ Law. We know the exiting intensity (S2 = 12.8) and we know the angle between the two polarizers (38 degrees). Plug in and solve for S1, the incident intensity.

5. If you stand 4 feet away from a plane mirror, how far away from your image in the mirror are you? Is your image real or virtual?

8 feet away, virtual. When you stand 4 feet away from a mirror, your image will appear to be behind the mirror (virtual) and 4 feet away from the mirror as well. That would put you and your image 8 feet apart. Plane mirrors always for virtual images.