Double Slit Experiment (Java-Applet)
The following Java-applet includes some experiments that can be started with the "automatic computation" button in the upper left. Waves appear from the left and pass through the two slits. Behind these, the waves spread out radially and steadily in all directions. Since this is not possible to draw, only two single radial rays are animated. By moving the slide on the right side further directions can be chosen. Simultaneously the intensity for the actual position is calculated and displayed on the screen.
The superposition of positive (wave crests) and negative (wave valleys) parts of the two waves leads to an intensification or an extinction of the intensity depending on the relative position of the two waves to each other. By using the "automatic" mode all directions are calculated and displayed by the program.
When the waves hit the detection screen the interference pattern (see below) becomes visible and shows the intensity distribution. The insertion with points of different colors illustrates the operations of the computer. Movement of the red and the blue points follows the amplitudes of the red and blue wave on the screen. The gray point is a sum of red and blue according to the sum of the amplitudes. As it is obvious that no negative values for the intensity on the screen are possible, the square of the sum of the amplitudes is used, as in quantum physics, so that there are no more negative values (represented by the black point as well as the interference pattern on the right).
This is the first attempt to explain the appearance of diffraction. Attentive observers might have noticed two things that are not explicable by the presented simplified model.
Though the frequency is variable the waves hit the screen always with a valley. It is possible to adjust the waves with the following sliding regulator so that they do not end with a valley on the screen any more. It is noticed that in the middle of the screen (marked by 0) the maximum diminishes or even disappears by adjusting the oscillation knots on the screen (sliding regulator for λ/4 to the very right).
Furthermore, the illustrated standing waves do not represent the motion in reality. Real waves move forward, the electromagnetic waves with the speed of light and the matter waves with a speed depending on their kinetic energy. Considering electromagnetic waves we do not see the changing amplitude but an average value. Speaking in mathematical terms, we need to calculate an integral over a wave-period. To depict the diffraction pattern of a forward moving wave please mark the selection-box "realistic".
This window shows the last period of the two waves before striking the screen, and is magnified for illustration.
We do not see a single point any more but a whole period. Again the gray graph is the sum of the red and the blue wave and the black graph is the square of the gray one. The mean value or, speaking in mathematical terms, the "time"-integral over this wave now represents the intensity on the screen. Moving the sliding regulator to change the oscillation valley and knots, you will recognize that the intensity distribution is not depending on the phase of the wave at the screen any more.
Coming to the end of this experiment we list two questions you could think about:
- Why are the patterns in a more "realistic" animation smoothened?
- Why do we obtain a constant intensity distribution when reducing the distance between the slits to zero?