will the distance between two sucessive bright or dark bands increase if the distance between coherent source is increased? and why or why not?

The distance between two successive bright or dark bands in an interference pattern is indeed affected by the distance between coherent sources. To understand this, we need to delve into the principles of wave interference and how the geometry of the setup influences the resulting pattern.

Understanding Interference Patterns

Interference patterns arise when two coherent light sources emit waves that overlap. These waves can constructively interfere, leading to bright bands, or destructively interfere, resulting in dark bands. The distance between these bands is determined by several factors, including the wavelength of the light and the geometry of the setup.

Key Factors Influencing Band Spacing

• Wavelength of Light: The distance between the bands is directly proportional to the wavelength. Longer wavelengths result in wider spacing between the bands.
• Distance Between Sources: Increasing the distance between the coherent sources affects the angle at which the waves meet at a screen, which in turn influences the spacing of the interference pattern.
• Distance to the Screen: The further the screen is from the sources, the more pronounced the spacing between the bands becomes.

Analyzing the Effect of Source Separation

When you increase the distance between the coherent sources, the angle at which the waves meet at the observation screen changes. This can be understood through the formula for the position of the interference fringes:

y = (mλL) / d

Where:

• y: Distance from the central maximum to the m-th order maximum
• m: Order of the maximum (0, 1, 2, ...)
• λ: Wavelength of the light
• L: Distance from the sources to the screen
• d: Distance between the two sources

From this equation, we can see that as the distance d between the sources increases, the spacing between the bright and dark bands (y) also increases, assuming the distance to the screen (L) and the wavelength (λ) remain constant.

Visualizing the Concept

Imagine two speakers playing the same note. If you move them further apart, the sound waves they produce will create a pattern of loud and soft spots in the room. The further apart the speakers are, the wider the spacing of those loud and soft spots becomes. This analogy helps illustrate how increasing the distance between coherent sources leads to a broader interference pattern.

Final Thoughts

In summary, increasing the distance between coherent sources does lead to an increase in the spacing between successive bright or dark bands in an interference pattern. This is due to the geometric relationships between the sources, the wavelength of the light, and the observation point. Understanding these relationships is crucial for grasping the principles of wave interference and its applications in various fields, including optics and acoustics.