A He-Ne laser beam is reflected from the surface of a CD onto a wall. The brightest spot is the reflected beam at an angle equal to the angle of incidence. However, fringes are also observed. If the wall is \(1.50 \mathrm{m}\) from the \(\mathrm{CD}\), and the first fringe is \(0.600 \mathrm{m}\) from the central maximum, what is the spacing of grooves on the CD?

The Helium-Neon (He-Ne) laser is a type of gas laser where the gain medium is a mixture of helium and neon gases. It operates by exciting the neon atoms to a higher energy state using a high voltage via helium atoms. This process leads to the emission of laser light, which is highly coherent, monochromatic, and well-collimated.

The He-Ne laser commonly emits at a wavelength of approximately 632.8 nanometers (nm), within the red portion of the visible light spectrum. This characteristic wavelength makes it suitable for a variety of applications, such as in our textbook problem where its coherent light is used to demonstrate optical principles like diffraction and interference on compact disc (CD) surfaces.

Diffraction is an optical effect that occurs when a wave, such as light, encounters an obstacle or a slit that is comparable in size to its wavelength. It results in the bending and spreading of the wave around the edges of the obstacle.

The classic example of diffraction is the pattern of bright and dark fringes observed when coherent light passes through a single slit or is reflected off closely spaced grooves, as in the CD example from our textbook problem. The pattern arises due to the constructive and destructive interference of the diffracted waves. The first fringe, or first-order maximum, occurs where the path difference between the diffracted waves is equal to one wavelength. The equation to quantify the diffraction pattern is given by the formula \(d \sin(\theta) = m\lambda\), where \(d\) is the spacing between grooves, \(\sin(\theta)\) is the sine of the angle of incidence, \(m\) is the order of maximum, and \(\lambda\) is the wavelength of the incident light.

Optics is the branch of physics that deals with the behavior and properties of light, including its interactions with matter, and the construction of instruments that use or detect it.

Optics can generally be divided into two branches: geometrical optics, which focuses on the approximation of light traveling in straight lines, and physical optics, which takes into account the wave nature of light. In the context of our CD groove spacing calculation, we delve into physical optics, considering phenomena such as wave interference and diffraction.

Understanding these optics principles allows us to solve complex problems like the one from our textbook, where we use the principles of diffraction and the properties of a He-Ne laser beam to calculate the groove spacing on a CD, a task that involves both understanding how light waves behave when encountering small structures, as well as how to apply mathematical formulas to describe these interactions.