One example is the generation and distribution of electrical energy that supports the entire infrastructure of the country. Nearly all modern power plants generate electricity via Faraday's law, which dates back to 1831. The ability of the human race to produce more power for a growing world population while reducing greenhouse emissions and a dependence on oil involves many physics issues, including the designs of new technologies such as ever more efficient solar cells and the invention of novel superconductors that could transmit energy long distances with little loss.
Another example is novel diagnostic devices for medical doctors that have helped many patients. As one example, physicists Edward Purcell and Felix Bloch were interested in studying fundamental properties of atomic nuclei when they invented the technique of nuclear magnetic resonance in the 1940s. Little did they dream that, decades later and after many refinements, their method would lead to magnetic resonance imaging, machines that allow high resolution non-invasive imaging of a living person's insides.
As one example, just think of the chain of discoveries starting with Galileo, who first used a telescope to observe the heavens and discovered that the leading beliefs that all objects in the sky orbited the Earth, and that all objects in the sky were perfect spheres were wrong. Then came Newton who showed theoretically that the intricate motions of various objects in the Solar System could be understood by his universal law of gravity together with his laws of motion. This was the first time that humans realized that it was possible to understand in precise detail phenomena that occurred beyond the Earth's surface, and further that there was a surprising simplicity and elegance to the laws of nature, and these same laws describe what happens on Earth.
Later, in the 1920s, came Edwin Hubble's astronomical discovery that all galaxies are moving away from Earth with speeds that increase linearly with distance from Earth. These data required Einstein's 1916 theory of general relativity to be understood, with two astonishing implications: the entire universe was not static but was expanding in volume, and, second, that the universe had a finite and immense age of about 14 billion years. The expansion of the universe in turn implied that the universe must have been much smaller in the past, and somehow burst into existence from a tiny region 14 billion years ago. The details of this Big Bang remain one of the greatest mysteries in all of science.
Further, nuclear physics led to an understanding of how stars get their energy via nuclear fusion. This led to the insight that the key elements besides hydrogen for Earth-like life (carbon, oxygen, nitrogen, calcium, phosphorus), which are created by stellar nucleosynthesis, should be found everywhere in the universe with about the same relative abundances as those observed in our solar system. This fact greatly increases the likelihood of Earth-like life existing beyond our solar system. How to invent telescopes that can detect the presence of life on the surfaces of planets that lie hundreds of light years away is yet another challenge that physicists are currently thinking about. The discovery of life outside our solar system would be another profound change in our understanding of the universe.
Few people outside of physics realize that the human race has made extraordinary progress in understanding the great diversity of phenomena observed on Earth and in the universe. Physicists and others have discovered concise, quantitatively accurate, and extremely useful mathematical descriptions of Nature such as the Maxwell equations that describe electromagnetic phenomena, the Einstein equations that describe gravity at the scale of solar systems and of the entire universe, the Schrodinger equation that describes the properties of all atoms, molecules, and solid materials, the Navier-Stokes equations that describe most fluid phenomena, and the Standard Model that clarifies and unifies the great diversity of behavior at the subatomic level.
It turns out that all the fundamental equations of nature can be written down on about three pages of paper. Experiments suggest that these three pages of equations are capable of describing all phenomena relevant to human civilization (biology, chemistry, material science, engineering, geology, meteorology, and so on) and most phenomena observed in the universe. Only in the limits of high energy (associated with the Large Hadron Collider and with the birth of the universe), or long times (associated with the expansion of the universe over ten billion years), or strong gravitational fields (black holes) or small length scales (much smaller than the diameter of a proton) are there phenomena that lie beyond the known equations of physics.
This extraordinary fact that so much complexity and detail can be understood (at least in principle) with just a few pages of equations gets to the heart of why physics is so interesting and intriguing, and why people who study physics are able to get a deeper sense of how the universe works. This fact however leaves open three big questions. One is why is it the case that our universe can be described with so few equations, and why do the equations have the form they do? A second question is whether it will be possible to find more even more concise theories in the future that describe an even broader range of phenomena? (If successful, string theory will be an example.) A third question is how to actually deduce and understand various phenomena from the known fundamental equations. For example, the Navier-Stokes equations are believed to describe Earth's atmosphere rigorously and yet no one has yet succeeded in deducing the existence or properties of clouds from these equations, despite these equations being known for over 170 years. The Schrodinger equation describes all possible behaviors of atoms and molecules and yet it is difficult to deduce many elementary facts of chemistry directly from this equation, and forget trying to deduce the existence of large molecular structures that reproduce themselves such as a living germ. How to deduce and understand basic observations from the fundamental equations is in fact a great on-going challenge in physics and often requires the invention of many new concepts and even new branches of physics like condensed matter physics.
One example is a calculation that students learn to carry out in the introductory quantum mechanics course Physics 464, which is the analytical solution of the Schrodinger equation for a hydrogen atom. The resulting expression for the hydrogen wave function can be intimidating at first glance (involving an infinite sum of spherical harmonics times generalized Laguerre polynomials), but provides much insight about the properties of atoms and why the periodic table has its particular form. The analytical solution shows that a hydrogen atom has a huge amount of structure that is entirely missed by the simple planetary orbit model of Niels Bohr that is taught in most high school science courses.
A second example is a calculation that students learn in the introductory course on thermal physics, Physics 363, which is to calculate in about two pages the approximate maximum possible mass of a white dwarf star (which is the eventual fate of about 97% of the stars in our galaxy). This maximum mass (called the Chandraskehar limit) turns out to be about 1.4 times the mass of our Sun and above this limit, the inward pull of gravity can no longer be opposed by the outward quantum mechanical pressure of the freely moving electrons in the core of the star. The result is that all white dwarfs that exceed this limit (usually by accumulating mass from a companion star in a binary star system) blow up (via fusion reactions of carbon nuclei) in the same way, with the same amount of brightness, with a blast of light that can be seen 10 billion light years from Earth. Telescopic observation of white dwarf explosions has played a crucial role in the discovery that the expansion of the universe is accelerating, which in turn led to the currently unsolved mystery of what is causing the accelerated expansion (called dark energy because no one knows what it is).