While the classical, wavelike behavior of light (interference and diffraction) has been easily observed in undergraduate laboratories for many years, explicit observation of the quantum nature of light (i.e., photons) is much more difficult. For example, while well-known phenomena such as the photoelectric effect and Compton scattering strongly suggest the existence of photons, they are not definitive proof of their existence. Here we present an experiment, suitable for an undergraduate laboratory, that unequivocally demonstrates the quantum nature of light. Spontaneously downconverted light is incident on a beamsplitter and the outputs are monitored with single-photon counting detectors. We observe a near absence of coincidence counts between the two detectors—a result inconsistent with a classical wave model of light, but consistent with a quantum description in which individual photons are incident on the beamsplitter. More explicitly, we measured the degree of second-order coherence between the outputs to be g(2)(0)=0.0177±0.0026, which violates the classical inequality g(2)(0)⩾1 by 377 standard deviations.
Thundercloud charge separation, or the process by which the bottom portion of a cloud gathers charge and the top portion of the cloud gathers the opposite charge, is still not thoroughly understood. Whatever the mechanism, though, a charge separation definitely exists and can lead to electrostatic discharge via cloud-to-cloud lightning and cloud-to-ground lightning. We wish to examine the latter form, in which upward leaders from Earth connect with downward leaders from the cloud to form a plasma channel and produce lightning. Much of the literature indicates that the lower part of a thundercloud becomes negatively charged while the upper part becomes positively charged via convective charging, although the opposite polarity can certainly exist along with various, complex intra-cloud currents. It is estimated that >90% of cloud-to-ground lightning is “negative lightning,” or the flow of charges from the bottom of the cloud, while the remaining <10% of lightning strikes is “positive lightning,” or the flow of charges from the top of the cloud. We wish to understand the electric potential surrounding charged thunderclouds as well as the resulting charge density on the surface of Earth below them. In this paper we construct a simple and adaptable model that captures the very basic features of the cloud/ground system and that exhibits conditions favorable for both forms of lightning. In this way, we provide a practical application of electrostatic dipole physics as well as the method of images that can serve as a starting point for further modeling and analysis by students.
These are functions that are not algebraic. The set of transcendental functions includes the trigonometric, inverse trigonometric, exponential and logarithmic functions, but it also includes a vast number of other functions that have never been named…. (Stewart 1999, p. 35)
We follow a radioactive sample from production in a reactor to its use in a biological application to model the complexities in the use of radioactive isotopes from a student’s perspective. Specifically, we describe a way to use gamma ray detection outside the body to estimate the clearance rate of these radioisotopes from the body and how that rate can be used to assess thyroid cancer remnant mass. This procedure has a long history in nuclear medicine and is well established. Classroom discussion questions are included to think more deeply about the proper (and improper) handling of radiopharmaceuticals as well as patient safety.
Similar to how stealth materials were developed to reduce the radar wave energy returning from an aircraft, here we explore a low-cost laboratory demonstration that uses similar principles to prevent detection of an object by an ultrasonic sensor. This demonstration setup can be used as a starting point to encourage students to explore the surface properties of materials and the ways in which ultrasonic ranging sensors operate.
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