91影视

Given data:

The refractive index of water is $n_1=\frac{4}{3}$

The refractive index of glass is $n_2=\frac{3}{2}$

The refractive index of air is$n_3=1$

Write the expression for the inverse of the transmission coefficient.

${\mathit{T}}^{\mathbf{-}\mathbf{1}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{4}{\mathbf{n}}_{\mathbf{1}}{\mathbf{n}}_{\mathbf{3}}}\left[{\left(n_1+n_3\right)}^2+\frac{\left(n_1^2-n_2^2\right)\left(n_3^2-n_2^2\right)}{n_2^2}si{n}^2\frac{n_2蝇d}{C}\right]$

Substitute localid="1657452458494" $n_1=\frac{4}{3},n_2=\frac{3}{2}$, and $n_3=1$in the above expression.

$T^{-1}=\frac{1}{4\left(\frac{4}{3}\right)\left(1\right)}\left[1+{\left(\frac{4}{3}\right)}^2+\frac{\left[{\left(\frac{4}{3}\right)}^2-{\left(\frac{3}{2}\right)}^2\left(r^2-{\left(\frac{3}{2}\right)}^2\right)\right]}{{\left(\frac{3}{2}\right)}^2}{\sin }^2\left(\frac{3蝇d}{2C}\right)\right]$

$T^{-1}=\frac{3}{16}\left[\frac{49}{9}+\frac{\left(\frac{-17}{36}\right)\left(-\frac{5}{4}\right)}{\left(\frac{9}{4}\right)}{\sin }^2\frac{3蝇d}{2C}\right]$

$T^{-1}=\frac{3}{16}\left[\frac{49}{9}+\left(\frac{17}{36}\right)脳\left(\frac{5}{4}\right)脳\left(\frac{4}{9}\right){\sin }^2\left(\frac{3蝇d}{2C}\right)\right]$

$T^{-1}=\frac{49}{48}+\frac{85}{\left(48\right)\left(36\right)}{\sin }^2\left(\frac{3蝇d}{2C}\right)$ 鈥︹�� (1)

For transmission coefficient to be minimum,localid="1657452777022" ${\sin }^2\frac{3蝇d}{2C}=1$

Substitute ${\sin }^2\frac{3蝇d}{2C}=1$in equation (1).

localid="1657453325025" role="math" $$\begin{gathered} T_{\min }=\frac{48}{49+\frac{85}{36}} \\ {T}_{min}=0.93455 \end{gathered}$$

For transmission coefficient to be minimum, ${\sin }^2\frac{3蝇d}{2C}=0$

Substitute ${\sin }^2\frac{3蝇d}{2C}=0$in equation (1).

$T_{\max }=\frac{48}{49}$

localid="1657453029338" $T_{\max }=0.987959$

On interchanging the values of $n_1$and $n_3$, there will be no change in the transmission coefficient equation. Hence, it is clearly seen that fish sees you just as well as you see it.

Therefore, the minimum and maximum transmission coefficients are localid="1657453345104" $T_{min}=0.93455$and$T_{\max }=0.987959$respectively, and it is clearly seen that fish sees you just as well as you see it.