91影视

The energy Eof a photon of wavelength $位$ is given by,

$E=\frac{hc}{位}$ 鈥︹��. (1)

Here, h is Planck鈥檚 constant, and c is the speed of light.

Let $R_{emit}$be the photon emission rate, then the absorption rate ${\mathrm{R}}_{\mathrm{abs}}=4.00{\mathrm{s}}^{-1}$in terms of the area of the eye ${\mathrm{A}}_{\mathrm{abs}}=2.00脳{10}^{-6}{\mathrm{m}}^2$

$R_{\mathrm{abs}}=\frac{P_{\mathrm{abs}}}{E_p}$

Since the detector absorbs only of the incident light, then the absorbed power is,

$\begin{array}{c}{P}_{\mathrm{abs}}=\left(\frac{80}{100}\right)I{A}_{\mathrm{abs}}\\ R_{\mathrm{abs}}{E}_p=\left(0.8\right)\left(\frac{P_{\mathrm{emit}}}{A_{\mathrm{emit}}}\right)A_{\mathrm{abs}}\\ P_{\mathrm{emit}}=\frac{R_{\mathrm{abs}}{E}_p}{0.8}\left(\frac{4蟺r^2}{A_{\mathrm{abs}}}\right)\end{array}$....(2)

Substitute the below values in eq. 1

$$\begin{gathered} \mathrm{位}=500\mathrm{nm}. \\ \mathrm{h}=6.626脳{10}^{-34}\mathrm{J}.\mathrm{s} \\ \mathrm{c}=3脳{10}^8\mathrm{m}/\mathrm{s} \end{gathered}$$

$$\begin{gathered} {\mathrm{E}}_{\mathrm{p}}=\frac{\left({\displaystyle 6.626脳{10}^{-34}\mathrm{J}.\mathrm{s}}\right)\left(3脳{10}^8\mathrm{m}/\mathrm{s}\right)}{500\mathrm{nm}} \\ =\frac{\left(6.626脳{10}^{-34}\mathrm{J}.\mathrm{s}\right)\left(3脳{10}^8\mathrm{m}/\mathrm{s}\right)}{\left(500\mathrm{nm}\right)\left({\displaystyle \frac{1\mathrm{m}}{{10}^9\mathrm{nm}}}\right)} \\ =3.93脳{10}^{-19}\mathrm{J}. \end{gathered}$$

Substitute the below values in eq. 2.

$$\begin{gathered} {\mathrm{R}}_{\mathrm{abs}}=4.00{\mathrm{s}}^{-1} \\ {\mathrm{E}}_{\mathrm{p}}=3.93脳{10}^{-19}\mathrm{J}. \\ {\mathrm{A}}_{\mathrm{abs}}=2.00脳{10}^{-6}{\mathrm{m}}^2 \\ \mathrm{r}=3\mathrm{m} \end{gathered}$$

$$\begin{gathered} P_{\mathrm{emit}}=\frac{\left({\displaystyle 4.00{\mathrm{s}}^{-1}}\right){\displaystyle \left(3.93脳{10}^{-19}\mathrm{J}\right)}}{0.8}\left(\frac{4\mathrm{蟺}{\left(3\mathrm{m}\right)}^2}{{\displaystyle 2.00脳{10}^{-6}{\mathrm{m}}^2}}\right) \\ =1.1脳{10}^{-10}\mathrm{W} \end{gathered}$$

Therefore, the emitter emits power ${\mathrm{1.1脳10}}^{-10}\mathrm{W}$.