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.
a. 2
b. 4
c. 4
do you have answer for problem 11?
nope :( for 10 nor 11...any help?
Problem 10: 3/4
Problem 11: a=3/5, b=8/10
anything for 12 and 13?
prob 11:
its a=3/5 as the probability of occurrence of |0> is 9/25
with normalisation, we find out
b=4/5
To calculate the intensity at the point in question when both slits are open for each of the three cases (bullet, wave, quantum mechanics), we need to understand some fundamental concepts and equations related to the double-slit experiment.
First, let's define the variables:
I_single_slit = Intensity at the point when either slit is open
I_both_slits = Intensity at the point when both slits are open
Now, let's consider each case separately.
(a) Bullet:
In the case of a bullet, we have classical physics laws at play. When either of the slits is open, the bullet will only pass through that open slit, and the intensity at the point will be I_single_slit. However, when both slits are open, we can treat them as separate paths that do not interfere with each other. Hence, the intensity at the point will be the sum of I_single_slit for each individual slit, giving us:
I_both_slits = I_single_slit + I_single_slit = 2 * I_single_slit
So, in this case, the intensity at the point when both slits are open is twice the intensity when either slit is open.
(b) Wave:
In the case of a wave, such as water or sound waves, interference patterns occur due to the superposition of waves from different slits. Here, we need to consider the concept of wave superposition and the principle of superposition to calculate the intensity at the point when both slits are open.
The intensity of a wave is proportional to the square of its amplitude. When either of the slits is open, the wave's amplitude at the point in question is √I_single_slit. However, when both slits are open, we need to consider the interference of waves. The waves from each slit will superpose, leading to constructive or destructive interference at different points on the final screen.
For the central point equidistant from both slits, we have constructive interference, resulting in an increased intensity compared to when either slit is open. The exact intensity at this point can be calculated using the equation for constructive interference:
I_both_slits = 4 * I_single_slit
So, in the case of waves, the intensity at the point when both slits are open is four times the intensity when either slit is open.
(c) Quantum Mechanics (Photons or Electrons):
In quantum mechanics, particles such as photons or electrons exhibit wave-particle duality. The double-slit experiment with particles shows interference patterns similar to those created by waves.
The intensity in the quantum mechanics scenario depends on the probability of finding a particle at a specific point. The probability, in turn, is related to the square of the wave function, which describes the particle's behavior. When either of the slits is open, the wave function and its square amplitude at the point are given by √I_single_slit.
When both slits are open, quantum mechanics predicts an interference pattern. In the case of the central point, the interference is again constructive, leading to an increased intensity compared to when either slit is open. However, the exact intensity at this point depends on the specific characteristics of the particle and its wave function.
To calculate the intensity at the point when both slits are open in this case, one would need to solve the quantum mechanical equations specific to the particle and the double-slit experiment setup. The equation would involve the wave functions and their superposition.
In summary, for the three cases:
(a) Bullet: I_both_slits = 2 * I_single_slit
(b) Wave: I_both_slits = 4 * I_single_slit
(c) Quantum Mechanics: The intensity at the point would require solving specific quantum mechanical equations for the particle and the double-slit experiment setup.