A student sets up a laser and screen and a single slit and observes the diffraction pattern. They then replace the single slit with a double slit (the separation of the double slit is exactly the width of the single slit). No other changes are made.

What differences and what similarities will there be between the old and new interference pattern?

To understand the differences and similarities between the old and new interference patterns when a single slit is replaced with a double slit, we need to consider the fundamental principles of diffraction and interference.

Diffraction is the bending of light waves around obstacles or through narrow openings. When a laser beam passes through a single slit, it diffracts, resulting in a diffraction pattern characterized by a central bright fringe surrounded by alternating dark and bright fringes.

Interference occurs when two or more waves overlap, resulting in constructive or destructive interference. In the case of the double slit, the light passing through both slits creates two separate coherent sources of light waves that interfere with each other on a screen, creating an interference pattern.

Now, considering the scenario where the separation of the double slit is exactly the width of the single slit, here are the differences and similarities between the old and new interference patterns:

Differences:
1. Number of fringes: In the single-slit diffraction pattern, there is only one central maximum and alternating dark and bright fringes on either side. However, in the double-slit interference pattern, multiple parallel bright fringes (known as interference fringes or interference bands) are produced, with dark regions in between.

2. Intensity distribution: The intensity of the bright fringes in the double-slit interference pattern tends to be more uniform and evenly distributed compared to the single-slit diffraction pattern. The interference fringes exhibit a series of maxima and minima, resulting in a complex pattern of light and dark regions.

3. Interference pattern spacing: The spacing between the bright fringes in the double-slit interference pattern is generally wider compared to the spacing between the bright and dark fringes in the single-slit diffraction pattern. This is because the double-slit consists of two coherent sources, allowing for greater interference effects.

Similarities:
1. Central maximum: Both the single-slit and double-slit setups will have a central bright fringe along the centerline of the screen. However, in the double-slit pattern, this central maximum is usually more intense compared to the single-slit pattern due to constructive interference.

2. Overall pattern shape: Both the single-slit diffraction pattern and the interference pattern of the double-slit setup exhibit a gradual decrease in intensity as we move away from the central maximum.

It is important to note that the above differences and similarities are specific to the given scenario where the separation of the double slit is exactly equal to the width of the single slit. Varying the separation distance or the width of the single slit will introduce further changes to the diffraction and interference patterns.