At what angle is the first-order maximum for 450-nm wavelength blue light falling on double slits separated by \(0.0500 \mathrm{mm} ?\)

Wavelength is a fundamental characteristic of light and has significant implications in the study of optics, especially in phenomena like double-slit interference. When we speak of the wavelength of light, we are referring to the distance between consecutive peaks of the light wave, which determines its color and is measured in nanometers (nm) for visible light. Different colors of light have different wavelengths; for instance, blue light typically has a wavelength around 450 nm.

Understanding the wavelength is vital since it directly affects the interference pattern created when light passes through slits, as seen in our exercise with the blue light. Accurate knowledge of the wavelength allows us to predict and calculate patterns and angles of diffraction in interference experiments.

In the context of double-slit interference, first-order maximum refers to the first bright fringe observed on either side of the central bright fringe on the interference pattern. This is where constructive interference takes place, meaning the waves from each slit arrive in phase and add up to make a brighter light. The order number, symbolized as 'm', indicates the sequence of the maximum; 'm = 1' for first-order, 'm = 2' for second-order, and so on.

The position of this first bright fringe is intimately linked to the wavelength and the geometry of the slit layout. By knowing the order of the maximum and other variables, one can determine the angle or position of these bright fringes, thus moving one step closer to deciphering the underlying interference pattern.

The angle of diffraction, often denoted as \(θ\), is the angle at which light rays emerging from the slits spread out or bend. It is key to solving problems related to interference as it indicates where on a detection screen or surface the fringes will appear, including both the bright first-order maximum and subsequent minima and maxima. As seen in the solution to our exercise, we calculated this angle to understand where the first bright fringe would appear.

By calculating the angle of diffraction, we gain insight into how light behaves upon encountering obstacles or slits, which is essential in various technological applications like spectroscopy and the design of optical instruments.

An interference pattern is a hallmark of the wave nature of light and results from the superposition of light waves from different paths. When light encounters two closely spaced slits, it diffracts and produces a pattern of alternating bright and dark bands on a screen known as fringes. The bright fringes correspond to areas of constructive interference, while the dark fringes indicate destructive interference.

This pattern is not random but follows a predictable sequence based on the characteristics of the light and the slits. Interpreting an interference pattern gives valuable insights into the physical properties of light, including its wavelength and phase. In the double-slit interference setup from our textbook exercise, analyzing the pattern yielded the angle for the first-order maximum, showcasing the direct relationship between the pattern's geometry and the intervals of diffraction.