Week 35 (Apr. 22 - 26)
Reading: Interference of light waves (Chap. 37)
Key Topics: electromagnetic waves, intensity, interference, and polarization
Key Topics: electromagnetic waves, intensity, interference, and polarization
Lab: Measuring the width of human hair using laser light interference. Here are the images for various students' hair:
Ed hair data, Dora hair data, Oliva hair data, Leah hair data, Von hair data
From these images, you can determine the distance of the center of each interference maximum (bright spot) from the center of the central bright spot. Using these measurements, along with the distance from the hair to the white screen, you can determine the angle, theta, of each bright spot. In your lab report, you must include at least two plots. Each should show data from one person's hair. The plot should have n on the x-axis and sin(theta_n) on the y-axis. Is the data linear? If so, how do you determine the hair width from the slope? Hint: young's two-slit interference maxima occur whenever sin(theta) = n * lambda / d, where d is the spacing of the slits.
Homework Problems:
Ed hair data, Dora hair data, Oliva hair data, Leah hair data, Von hair data
From these images, you can determine the distance of the center of each interference maximum (bright spot) from the center of the central bright spot. Using these measurements, along with the distance from the hair to the white screen, you can determine the angle, theta, of each bright spot. In your lab report, you must include at least two plots. Each should show data from one person's hair. The plot should have n on the x-axis and sin(theta_n) on the y-axis. Is the data linear? If so, how do you determine the hair width from the slope? Hint: young's two-slit interference maxima occur whenever sin(theta) = n * lambda / d, where d is the spacing of the slits.
Homework Problems:
- Sunlight intensity: The intensity of sunlight is about 1000 Watts/square meter at the earth's surface. What is the amount of energy delivered during one hour to a 20 square meter solar panel? What is the amplitude of the electric field in the electromagnetic wave striking the solar panel? (Answer: 20,000 Joules per second * 3600 seconds = 72 MegaJoules.)
- Laser intensity: A Neodymium-glass laser emits short pulses of high-intensity electromagnetic waves. The electric field has an amplitude of 3e9 Newtons per coulomb. Find the average power of each pulse that passes through a 1.6e-5 square meter surface perpendicular to the laser beam. (Answer: the intensity is 1.19 e16 watts/m^2. So the power is 191e9 Joules or 191 GigaJoules.)
- Skip this problem (we didn't get to it): Speed of light measurement: Foucault's spinning mirror apparatus. Find the minimum rotation rate of mirror 1 so that light (speed 300,000 km / sec) enters the telescope after bouncing from mirror 2, which is 3 km away. The light source and the telescope, and the telescope and mirror 2 are each separated by 1 degree. (Answer: the light must travel 6km by the time the mirror has rotated half a degree. So the mirror needs to rotate half a degree in 20 microseconds. Minimum rotation rate is 69 rotations per second.)
- Skip this problem (we didn't get to it): Optional thin film interference problem: Thin film interference: A thin film of gasoline floats on a puddle of water. Sunlight falls almost perpendicularly on the puddle and reflects into your eyes. Although sunlight is white (it contains all colors), the film has a yellow hue since destructive interference eliminates the colors of blue (469 nm in vacuum) from the reflected light. If the refractive index for light in gasoline and water are 1.40 and 1.33, respectively, then determine the minimum non-zero thickness of the film. What if the gasoline was on glass (n = 1.52) instead of water? (answer for part 1: 168 nm)