Final answer:
To ascertain whether the vertex from 3 is a minimum or maximum, one must consider the context of wave interference in physics, such as an experiment involving a diffraction grating or double-slit experiment.
Step-by-step explanation:
To determine whether the vertex from 3 is a minimum or maximum, we need to refer to the context of wave interference, typically in the subject of physics. Based on the reference information provided, it appears this question relates to a wave interference pattern, possibly from a diffraction grating or a double-slit experiment.
The second-order maximum would occur at a position where the path difference between waves is equal to an integer multiple of the wavelength. Since the term “second-order” is used, we are referring to the second bright fringe (or maximum) on either side of the central maximum. From the significance section you provided, if the first-order maximum (also known as the principal maximum) is expected near β = 3π/2, then the third maximum would follow a similar pattern, increasing by an integer multiple of the wavelength for each subsequent maximum.
As for the angle of the first minimum, it would be the angle at which destructive interference occurs, such that the path difference between the two waves is equal to half a wavelength (or an odd multiple of half a wavelength).
The highest-order maximum possible would depend on the specifics of the experiment, such as the wavelength of the light, the separation of the slits, and the distance to the screen. Typically, as the angle increases, the intensity of the maxima decreases, and at some point, the maximum cannot be distinguished from the background light. Generally, the higher the order of the maximum, the less intense it becomes.
In regards to the CHECK YOUR UNDERSTANDING section, it seems to be part of an exercise that asks for the specific angle and relative intensity of the third maximum which typically follows the order of the maxima and would require calculations based on the experiment's parameters.