91影视

Diameter of pupil $d=3\text{mm}$

Wave length of light $\left(位\right)=550\text{nm}$

The Rayleigh criteria specify the minimal distance between two light sources that must exist in order to resolve them into separate objects.

Raleigh criterion for resolving with angular separation ${胃}_R$is $\sin {胃}_R=\frac{1.22位}{d}$

Diameter of pupil $d=3\text{mm}$

$$\begin{gathered} d=\text{3}\text{mm}\left(\frac{{10}^{-3}\text{m}}{\text{mm}}\right) \\ =3脳{10}^{-3}\text{m} \end{gathered}$$

Wave length of light $\left(位\right)=550\text{nm}$

$$\begin{gathered} d=550\text{nm}\left(\frac{{10}^{-9}\text{m}}{1\text{m}}\right) \\ =550脳{10}^{-9}\text{m} \end{gathered}$$

Also if D is a size of the object that eye resolve and L is distance between eye and object

Then we have the condition $\tan {胃}_R=\frac{D}{L}$

Here size of the object that eye resolved

$$\begin{gathered} D=60渭m \\ =60脳{10}^{-6}m \end{gathered}$$

As i${胃}_R$s small $\text{tan}{胃}_R鈮�\sin {胃}_R鈮�{胃}_R$

Therefore from above equations

$$\begin{gathered} \frac{D}{L}=\frac{1.22位}{d} \\ L=\frac{Dd}{1.22位} \end{gathered}$$

Substitute given values

$$\begin{gathered} L=\frac{\left(60脳{10}^{-6}鈥�\text{m}\right)\left(3脳{10}^{-3}\text{m}\right)}{1.22\left(550脳{10}^{-9}\text{m}\right)} \\ =0.27鈥�\text{m}\backslash \mathrm{hfill} \\ \text{= 0.27}鈥�\text{m}\left(\frac{100\text{cm}}{\text{m}}\right) \\ =27鈥�\text{cm} \end{gathered}$$

Hence, the value is $27cm$.