| @@ -1,21 +1,13 @@ |
| | | ### Statement |
| | | |
| | − | $12.1.17.$ |
| | + | $12.1.17.$ The thicker the film, the greater the amplitude of the electric field strength of an electromagnetic wave reflected from a conductive film. The figure shows a typical dependence of the reflected wave amplitude on the film thickness. Initially (in the region $x < x_1$), the amplitude linearly depends on the film thickness $x$, then the linear dependence is broken, and in the region $x > x_2$, the amplitude of the reflected wave differs little from the amplitude of the incident wave $E_0$. Explain this dependency. |
| | | |
| | − | The thicker the film, the greater the amplitude of the electric field strength of |
| | − | an electromagnetic wave reflected from a conductive film. The figure shows a |
| | − | typical dependence of the reflected wave amplitude on the film thickness. At |
| | − | the initial moment (in the region x < x1), the amplitude linearly depends on |
| | − | the film thickness x, then the linear dependence is broken, and in the region |
| | − | x > x2, the amplitude of the reflected wave differs little from the amplitude of |
| | − | the incident wave E0. Explain this dependency. |
| | + |  |
| | | |
| | | ### Solution |
| | | |
| | − | The behavior is explained by the interaction of the electromagnetic wave with the free electrons of the material. |
| | + | This behavior is explained by the interaction of the electromagnetic wave with the free electrons of the material. |
| | | |
| | − | For very small thicknesses (x < x_1), the film is semi-transparent. The incident wave penetrates completely and sets all the free electrons of the film into motion. The induced current, and therefore the re-emitted field (reflected wave), is proportional to the number of electrons and, consequently, to the thickness x. Hence, the reflected amplitude grows linearly with x. |
| | − | |
| | − | As the thickness increases (x_1 < x < x_2), it reaches a dimension comparable to the penetration depth (or skin depth) of the material at that frequency. The incident wave no longer manages to pass completely through the film; the induced current stops growing proportionally because the deeper layers contribute less and less. The growth of the reflected amplitude slows down, and the dependence is no longer linear. |
| | − | |
| | − | When the thickness greatly exceeds the penetration depth (x > x_2), the film behaves like a bulk conductor. The incident wave is almost completely attenuated before reaching the back face. All the non-dissipated energy is re-emitted backward, and the amplitude of the reflected wave asymptotically approaches the incident amplitude$ E_0$ Beyond this point, increasing the thickness practically does not change the reflection. |
| | + | 1. For very small thicknesses ($x < x_1$), the film is semi-transparent. The incident wave penetrates completely and sets all the free electrons of the film into motion. The induced current, and therefore the re-emitted field (reflected wave), is proportional to the number of electrons and, consequently, to the thickness $x$. Hence, the reflected amplitude grows linearly with $x$. |
| | + | 2. As the thickness increases ($x_1 < x < x_2$), it reaches a dimension comparable to the penetration depth (skin depth) of the material at that frequency. The incident wave no longer passes completely through the film without attenuation; the deeper layers are shielded and contribute less and less to the induced current. The growth of the reflected amplitude slows down, and the dependence is no longer linear. |
| | + | 3. When the thickness greatly exceeds the penetration depth ($x > x_2$), the film behaves like a bulk conductor. The incident wave is almost completely attenuated before reaching the back face. All the non-dissipated energy is re-emitted backward, and the amplitude of the reflected wave asymptotically approaches the incident amplitude $E_0$. Beyond this point, increasing the thickness practically does not change the reflection. |
