When light interacts with an obstacle or an aperture, it tends to bend around the edges, creating a phenomenon called diffraction. This bending of light results in a characteristic pattern of bright and dark fringes known as a diffraction pattern. The nature of this pattern, specifically the width and spacing of the fringes, is highly dependent on the wavelength of the light used.

Diffraction and Wavelength Relationship

The extent to which light diffracts is directly proportional to its wavelength. In simple terms, longer wavelengths diffract more significantly than shorter wavelengths. For a single-slit diffraction setup, the angular position of the dark fringes (minima) is given by the formula:

\[ a \sin\theta = n\lambda \]

Where:

• \(a\) represents the width of the slit.
• \(\theta\) is the angle of diffraction from the central maximum.
• \(n\) is an integer (1, 2, 3, ...) representing the order of the minimum.
• \(\lambda\) is the wavelength of the light.

For small angles, which is often the case in diffraction experiments, \(\sin\theta \approx \theta\). Thus, the angular position becomes approximately \(\theta \approx \frac{n\lambda}{a}\). If a screen is placed at a distance \(D\) from the slit, the linear distance of the \(n\)-th minimum from the center (\(x_n\)) can be approximated as \(x_n \approx D\theta\). Substituting the value of \(\theta\):

\[ x_n \approx \frac{n\lambda D}{a} \]

From this approximation, it is evident that the position of the fringes, and consequently the spacing between them (also known as fringe width), is directly proportional to the wavelength (\(\lambda\)) of the light. This means if the wavelength increases, the fringes will be further apart and the overall pattern will appear broader.

Comparing Violet Light and Green Light

The question describes a scenario where violet light is replaced by green light. To understand the effect, we need to compare the wavelengths of these two colors:

• Violet light has one of the shortest wavelengths in the visible spectrum, typically ranging from approximately 380 nm to 450 nm.
• Green light has a longer wavelength than violet light, typically ranging from approximately 495 nm to 570 nm.

Therefore, when a student replaces violet light with green light, they are essentially increasing the wavelength of the light source used in the diffraction experiment (\(\lambda_{\text{green}} > \lambda_{\text{violet}}\)).

Impact on Diffraction Pattern

Given that the wavelength of green light is greater than that of violet light, and knowing that the fringe spacing in a diffraction pattern is directly proportional to the wavelength, the following changes will occur:

• The bright fringes in the pattern will become broader.
• The dark regions between the bright fringes will also expand.
• As a result, the entire diffraction pattern will appear more spread out, and the fringes will be seen further apart from each other.

This effect is a direct consequence of the increased wavelength causing the light waves to bend more significantly as they pass through the slit or around the obstacle.

Conclusion on Light Replacement

In summary, when the student replaces the violet-colored beam of light with a green-colored beam of light, the wavelength of the light increases. This increase in wavelength causes the diffraction pattern to become broader and further apart, as the fringe width and spacing are directly proportional to the wavelength of the light.