My thoughts on the problems in workshop # 11
1: A two-slit interference experiment is set up, and the fringes are displayed on a screen. Then the whole apparatus is immersed in a swimming pool. How does the fringe pattern change?
Moderately difficult conceptual problem on interference.
2: An FM radio station has a frequency of 103.5 MHz and uses two identical antennas mounted at the same elevation, 15.0 m apart. The antennas radiate in phase. The resulting radiation pattern has a maximum intensity along a horizontal line that is perpendicular to the line joining the antennas and midway between them. Assuming that the intensity is observed at distances from the antennas that are much larger than 15.0 m a) At what other angles (measured from the line of maximum intensity) is the intensity maximum? b) At what angles is it zero?
Interference in a different system. Low to moderate difficulty.
3: Monochromatic light is directed at normal incidence on a thin film. There is destructive interference for the reflected light, so its intensity is very low. What happened to the energy of the incident light? How does this relate to the need for coatings on a camera lens?
I LOVE these mind-twisting conceptual problems. This is discussed on p.1153 of your text.
4: Two rectangular pieces of plane glass are laid one upon the other on a table. A thin strip of paper is placed between them at one edge so that a very thin wedge of air is formed. The plates are illuminated at normal incidence by light from a sodium lamp (l o=589 nm). Interference fringes are formed, with 16.0 fringes per centimeter. Find the angle of the wedge.
Again, interference in a system different from the classic two-slit experiment. Get the hint … you are better off understanding how to derive interference relations from first principles than you are memorizing two-slit equations!!!!
5: The human ear is especially sensitive to sounds at frequencies around 3500 Hz. Show that this can be understood by regarding the ear’s auditory canal, which extends about 2.5 cm from the outside ear to the eardrum, as a "nonreflecting coating" for sound. … waves is waves! Ain’t this cool?
This takes you out of the classic thin film optics problem area … but waves is waves! Moderate difficulty
6: A plane transmission grating has 4000 slits/cm. Assume normal incidence. The a and d lines emitted by atomic hydrogen have wavelengths 656 nm and 410 nm, respectively. Compute the angular separation in degrees between these lines in a) the first order spectrum and b) the second order spectrum.
Somewhat involved plug and chug using gratings. Important to those of you who make use of spectroscopy.
7: Now for a little head stretching … You devise a two slit interference experiment with a laser that is capable of VERY fine intensity tuning. In a completely dark room, you shine the laser on two slits and record a classic 2-slit interference fringe pattern on a screen of film some distance away. Now, you turn down the intensity of the laser until it emits only one photon at a time. After some time passes, so that the integrated number of photons coming out of the laser is large, you develop the film. What kind of pattern do you observe on the film?
Wave particle duality is conceptually quite difficult to deal with. But this is the kind of thing that makes physics fun!