91影视

Write the expression for the reflection coefficient for light to conducting surface.

$\mathit{R}\mathbf{=}{\mathbf{\left|}\frac{{\stackrel{\mathbf{~}}{\mathbf{E}}}_{{\mathbf{0}}_{\mathbf{R}}}}{{\stackrel{\mathbf{~}}{\mathbf{E}}}_{{\mathbf{0}}_{\mathbf{I}}}}\mathbf{\right|}}^{\mathbf{2}}\mathbf{=}{\mathbf{\left|}\frac{\mathbf{1}\mathbf{-}\stackrel{\mathbf{~}}{\mathbf{尾}}}{\mathbf{1}\mathbf{+}\stackrel{\mathbf{~}}{\mathbf{尾}}}\mathbf{\right|}}^{\mathbf{2}}$ 鈥︹�� (1)

Here,$尾$ is the complex quantity which is given as:

$\begin{array}{c}\widetilde{尾}=\frac{{渭}_1{v}_1}{{渭}_2蝇}{\tilde{k}}_2\\ \widetilde{尾}=\frac{{渭}_1{v}_1}{{渭}_2蝇}(k_2+i{K}_2)\end{array}$ 鈥︹�� (2)

Write the value of the wave number$k_2$ .

$k_2=蝇\sqrt{\frac{{蔚}_2{渭}_2}{2}}{[\sqrt{1+{\left(\frac{蟽}{{蔚}_2蝇}\right)}^2}+1]}^{\frac{1}{2}}$

Write the value of the wave number$k_2$ .

$K_2=蝇\sqrt{\frac{{蔚}_2{渭}_2}{2}}{[\sqrt{1+{\left(\frac{蟽}{{蔚}_2蝇}\right)}^2}鈭�1]}^{\frac{1}{2}}$

As silver is a good conductor then$蟽>>{蔚}_2蝇$, .

The value of$k_2$ and $k_2$will be,

$\begin{array}{c}{k}_2=蝇\sqrt{\frac{{蔚}_2{渭}_2}{2}}\sqrt{\left(\frac{蟽}{{蔚}_2蝇}\right)}\\ K_2=蝇\sqrt{\frac{{蔚}_2{渭}_2}{2}}\sqrt{\left(\frac{蟽}{{蔚}_2蝇}\right)}\end{array}$

Hence, the value of$k_2$ and $k_2$becomes,

$k_2=K_2=\sqrt{\frac{蝇{渭}_2蟽}{2}}$

Substitute $k_2=K_2=\sqrt{\frac{蝇{渭}_2蟽}{2}}$in equation (2).

$\begin{array}{c}\widetilde{尾}=\frac{{渭}_1{v}_1}{{渭}_2蝇}\sqrt{\frac{蟽{渭}_2蝇}{2}}(1+i)\\ \widetilde{尾}={渭}_1{v}_1\sqrt{\frac{蟽}{2{渭}_2蝇}}(1+i)\end{array}$ 鈥︹�� (3)

Here,

$\begin{array}{c}纬={渭}_1{v}_1\sqrt{\frac{蟽}{2{渭}_2蝇}}\\ 纬={渭}_{0}c\sqrt{\frac{蟽}{2{渭}_0蝇}}\end{array}$

Substitute $纬={渭}_1{v}_1\sqrt{\frac{蟽}{2{渭}_2蝇}}$and $纬={渭}_{0}c\sqrt{\frac{蟽}{2{渭}_0蝇}}$in equation (3).

$\begin{array}{c}\widetilde{尾}={渭}_{0}c\sqrt{\frac{蟽}{2{渭}_0蝇}}(1+i)\\ \widetilde{尾}=c\sqrt{\frac{蟽{渭}_0}{2蝇}}(1+i)\end{array}$

Substitute$c=3脳{10}^8\text{鈥尘}/\text{s}$ ,$蟽=6脳{10}^7\text{鈥�}{\left(惟\text{m}\right)}^{鈭�1}$ , ${渭}_0=4蟺脳{10}^{鈭�7}\text{鈥塇}/\text{m}$and $蝇=4脳{10}^{15}{\text{鈥塻}}^{鈭�1}$in the above expression.

$\begin{array}{c}\widetilde{尾}=(3脳{10}^8\text{鈥尘/s})\sqrt{\frac{(6脳{10}^7\text{鈥�}{\left(惟\text{m}\right)}^{鈭�1})(4蟺脳{10}^{鈭�7}\text{鈥塇/尘})}{2(4脳{10}^{15}{\text{鈥塻}}^{鈭�1})}}(1+i)\\ \widetilde{尾}=29(1+i)\end{array}$

Substitute i$\widetilde{尾}=29(1+i)$n equation (1).

$\begin{array}{c}R={\left|\frac{1鈭�29(1+i)}{1+29(1+i)}\right|}^2\\ R=\frac{{(1鈭�29)}^2+{\left(29\right)}^2}{{(1+29)}^2+{\left(29\right)}^2}\\ R=0.93\end{array}$

Therefore, the reflection coefficient for light at an air air-to-silver interface is$93\%$ .