91影视

The special difference between constructive and destructive interference is that when the displacements of the waves that meet are in the same direction, whereas destructive interference occurs when displacements of the waves that meet are in the opposite directions.

(a)

We may find the slit separation in terms of the provided quantities by using the double-slit interference relation (m and v)

$\text{诲蝉颈苍(胃)=}\left(\text{n+}\frac{\text{1}}{\text{2}}\right)\text{位}$

$\text{位=}\frac{\text{h}}{\text{p}}$

$\text{d=}\frac{\left(\text{n+}\frac{\text{1}}{\text{2}}\right)\text{h}}{\text{蝉颈苍(胃)辫}}$

$\text{苍=0,鈥塻颈苍(30)=}\frac{\text{1}}{\text{2}}\text{,鈥塸=尘惫}$

$\text{d=}\frac{\text{h}}{\text{mv}}$

Let's look at the data in the problem: 100 electrons per second are observed with slit one alone open (the corresponding wave is.${\text{蠄}}_{\text{1}})$However, with slit two open, 36 electrons per second are detected at the first minimum (the corresponding wave is${\text{蠄}}_{\text{2}})$. When the two waves destructively interfere with each other, this minimum occurs$\left({\text{蠄}}_{\text{1}}{\text{-蠄}}_{\text{2}}\right)$

$\begin{array}{l}{\left|{\text{蠄}}_{\text{1}}\right|}^{\text{2}}鈭�\text{100}\\ \left|{\text{蠄}}_{\text{1}}\right|鈭�\text{10}\end{array}$

and

$\begin{array}{l}{\left|{\text{蠄}}_D\right|}^{\text{2}}鈭�36\\ \left|{\text{蠄}}_D\right|鈭�卤6\end{array}$

For destructive interference, we can write,

$\begin{array}{l}\left|{\text{蠄}}_{\text{D}}\right|鈭�\left|{\text{蠄}}_1\right|鈭�\left|{\text{蠄}}_2\right|\\ \left|{\text{蠄}}_2\right|鈭�\left|{\text{蠄}}_{\text{D}}\right|+\left|{\text{蠄}}_1\right|\\ \left|{\text{蠄}}_{\text{2}}\right|鈭�10卤6\end{array}$

$\begin{array}{c}{\left|{{\text{蠄}}_{\text{2}}}^{\text{'}}\right|}^2鈭�{\left(16\right)}^2\\ 鈭�256\end{array}$

$\begin{array}{c}{\left|{{\text{蠄}}_{\text{2}}}^{\text{'}\text{鈥�}\text{'}}\right|}^2鈭�{\left(4\right)}^2\\ 鈭�16\end{array}$

The number of electrons per second in a particular area for slit 2 can be either 16 electrons per second or 256 electrons per second.

The constructive interference means the addition of the two-slit wave functions together. As we already have the amplitude of each wave we can directly find the total number of electrons detected per second in a given area for each case of part b).

Therefore, considering both possibilities discussed in part (b), we can write,

For$\left|{{\text{蠄}}_{\text{2}}}^{\text{'}}\right|$

$\begin{array}{c}{\left|{\text{蠄}}_{\text{1}}{{\text{+蠄}}_{\text{2}}}^{\text{'}}\right|}^{\text{2}}鈭�{\left(\text{10+16}\right)}^{\text{2}}\\ 鈭�{\left(\text{26}\right)}^{\text{2}}\\ 鈭�\text{676}\end{array}$

For

$\begin{array}{c}{\left|{\text{蠄}}_{\text{1}}{{\text{+蠄}}_{\text{2}}}^{\text{'}\text{鈥�}\text{'}}\right|}^{\text{2}}鈭�{\left(\text{10+4}\right)}^{\text{2}}\\ 鈭�{\left(\text{14}\right)}^{\text{2}}\\ 鈭�\text{256}\end{array}$

(a)In terms of the provided quantities, slit separation is$\text{d=}\frac{\text{h}}{\text{mv}}$

(b) The number of electrons per second in a particular area for slit 2 can be either 16 electrons per second or 256 electrons per second.

(c) With both slits open, a signal was caught at the central detector is either 196 or 676 electrons per second.