A laser used in retinal surgery emits photons of wavelength \(632.8 \mathrm{~nm}\) in pulses of \(0.5 \mathrm{~W}\) that last \(2 \times 10^{-2} \mathrm{~s}\). The number of photons in each pulse is nearest to (A) \(10^{10}\) (B) \(10^{15}\) (C) \(10^{20}\) (D) \(10^{25}\) (E) \(10^{30}\)

Laser physics is the branch of optics that deals with the understanding and application of lasers. Lasers, which stand for Light Amplification by Stimulated Emission of Radiation, emit light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. Unlike ordinary light sources, which emit a broad spectrum of light, lasers emit light in a specific, coherent wavelength, making them highly focused and precise.

This coherent light is particularly useful in various applications such as retinal surgery, where lasers must be precise enough to target very small areas without damaging surrounding tissue. In our exercise, the laser emits photons at a precise wavelength of 632.8 nm. The laser's precision and the ability to generate high intensity in a directed beam are quintessentially what makes laser physics an essential field in modern medicine and technology.

The energy of a photon is calculated based on its wavelength or frequency. This energy determination is critical in fields such as quantum mechanics, astronomy, and any science involving electromagnetic radiation. For example, in the exercise, to determine the energy of photons emitted by a laser for retinal surgery, we use the formula:

\(E_{photon} = \frac{hc}{\lambda}\)

where \(E_{photon}\) is the energy of a single photon, \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the photon's wavelength. This formula underpins the quantum mechanical relationship between energy and electromagnetic waves, illustrating that light has both wave-like and particle-like properties, a central concept in quantum physics.

Planck's constant (\(h\)) is a fundamental constant in physics that plays a crucial role in quantum mechanics. It is the proportionality constant that relates the energy (\(E\)) of a photon to its frequency (\(u\)): \(E = hu\). It's also involved in the equation for calculating photon energy when the wavelength is known, as seen in the practice problem.

Planck's constant has a value of approximately \(6.626 \times 10^{-34}~\mathrm{Js}\), which indicates the very small energy scales typical in quantum processes. It forms the bedrock for much of our understanding of atomic and subatomic processes, including the behavior of photons in laser light. Moreover, Planck's constant usage not only includes energy calculations but also operations such as quantifying action in physical systems, establishing a limit to the precision with which certain pairs of physical properties, known as complementary variables, like position and momentum, can be known simultaneously – a concept known as the Heisenberg uncertainty principle.