why do you find the same wavelengths and colors on each side of the central maxima?
In what experiment? Single slit diffraction of white light? Diffraction by a grating?
Because cos(theta) = cos(-theta)
Theta is the angular distance from the central maximum, for a particular wavelength and order.
The phenomenon you are referring to is known as the central maxima in the context of wave interference and diffraction. It occurs when waves diffract and interfere with each other as they pass through a narrow slit or around an obstacle.
To understand why you find the same wavelengths and colors on each side of the central maxima, we need to consider the concept of constructive and destructive interference.
When waves pass through a slit or obstacle, they spread out and interfere with each other. In the case of a single slit, the central maxima is formed directly in line with the slit, while secondary maxima and minima are formed on either side. These secondary maxima and minima appear due to the constructive and destructive interference of the waves.
Now, let's focus on the central maxima. At this point, the waves from different sections of the slit arrive in phase, which means their crests and troughs align perfectly. As a result, they reinforce each other, leading to constructive interference.
When waves reinforce each other through constructive interference, they are in phase and have the same wavelength. This means that on each side of the central maxima, the waves from the different sections of the slit also arrive in phase and have the same wavelength. Consequently, we observe the same wavelengths and colors on each side of the central maxima.
In summary, the phenomenon of finding the same wavelengths and colors on each side of the central maxima is a result of the constructive interference of waves from different sections of the slit, which are perfectly in phase with each other.