In the double-slit experiment, consider the point at the middle of the final (detector) screen which is equidistant from the two slits. Suppose the intensity at that point is when either slit is open. Now for each of the three cases (a) bullet (b) wave (c) quantum mechanics (photons or electrons) calculate the intensity at the same point when both slits are open.

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To calculate the intensity at a particular point on the detector screen in the double-slit experiment, we need to understand the concepts of interference and superposition.

(a) In the case of a bullet, we are dealing with classical particles that do not exhibit wave-like behavior. Therefore, the concept of interference is not applicable in this case. When either slit is open, the bullet will pass through the respective slit and create a single impact point on the screen. When both slits are open, the bullet will pass through both slits simultaneously, but it will still create a single impact point on the screen. Consequently, the intensity at the point equidistant from the two slits remains the same whether one or both slits are open.

(b) If we consider the case of a wave, such as water waves or sound waves, both slits act as sources of secondary waves, and these waves interfere with each other when they meet. When either slit is open, only one wave is produced, and it spreads out and reaches the screen, producing a certain intensity at the equidistant point. However, when both slits are open, the two waves coming from the slits interfere with each other constructively or destructively, leading to an interference pattern on the screen. At the equidistant point, the intensity can vary depending on whether constructive or destructive interference occurs.

(c) In the case of quantum mechanics, which describes the behavior of particles at the atomic and subatomic level, such as photons or electrons, we observe wave-particle duality. When either slit is open, a single particle will pass through the respective slit and create an impact point on the screen, similar to the bullet case. However, when both slits are open, each particle behaves as a wave that passes through both slits simultaneously, resulting in an interference pattern on the screen.

To calculate the intensity at the equidistant point when both slits are open, we need to know the specific properties of the particles, such as the wavelength and the number of particles being used in the experiment. This information is required to determine the exact interference pattern and calculate the intensity at that specific point.