91影视

The slit separation,$d=1.73渭m$

The angles,$胃=卤17.6掳,37.3掳,-37.1掳,65.2掳,-65掳$

The condition for the maxima in diffraction to calculate the wavelength of the green light is given as follows.

$$\begin{gathered} dsin胃=m位 \\ 位=\frac{dsin胃}{m} \end{gathered}$$ .........(1)

Here, is the order of the diffraction and $\mathit{位}$is the wavelength.

Calculate the wavelength for $胃=-17.6掳$and $m=1$.

Substitute $1.73\mathrm{渭尘}$for $d$, $-17.6掳$ for $胃$, and 1 for$m$into equation (i).
$$\begin{gathered} 位=\frac{\left|1.73脳{10}^{-6}鈥�\text{m}脳\sin \left(-17.6\right)\right|}{1} \\ 位=0.523脳{10}^{-6}\text{m} \\ 位=\text{523}\text{nm} \end{gathered}$$

Calculate the wavelength for $17.6掳$and $m=1$

Substitute$1.73渭m$for$d$, $17.6掳$for $胃$, and 1 for m into equation (i).

$$\begin{gathered} 位=\frac{\left|1.73脳{10}^{-6}\text{m}脳\sin \left(17.6\right)\right|}{1} \\ 位=0.523脳{10}^{-6}\text{m} \\ 位=\text{523}\text{nm} \end{gathered}$$

Calculate the wavelength $胃=37.3掳$for and $m=2$.

Substitute $1.73渭m$for $d$, $37.3掳$for $胃$, and 1 for $m$into equation (i).

$$\begin{gathered} 位=\frac{\left|1.73脳{10}^{-6}\text{m}脳\sin \left(37.3\right)\right|}{2} \\ 位=0.524脳{10}^{-6}\text{m} \\ 位=\text{524}\text{nm} \end{gathered}$$

Calculate the wavelength for$胃=-37.1掳$and $m=2$.

Substitute $1.73渭m$for$d$, $-37.1掳$for$胃$, and 2 for $m$into equation (i).

$$\begin{gathered} 位=\frac{\left|1.73脳{10}^{-6}\text{m}脳\sin \left(-37.1\right)\right|}{2} \\ 位=0.522脳{10}^{-6}\text{m} \\ 位=\text{522}\text{nm} \end{gathered}$$

Calculate the wavelength for$胃=65.2掳$and $m=3$.

Substitute $1.73渭m$for $d$, $65.2掳$for $胃$, and 3 for $m$into equation

(i).

$$\begin{gathered} 位=\frac{\left|1.73脳{10}^{-6}\text{m}脳\sin \left(65.2\right)\right|}{3} \\ 位=0.523脳{10}^{-6}\text{m} \\ 位=\text{523}\text{nm} \end{gathered}$$

Calculate the wavelength for $胃=-65.掳$and $m=3$.

Substitute $1.73渭m$for $d$, $-65掳$for $胃$, and 3 for $m$into equation (i).

$$\begin{gathered} 位=\frac{\left|1.73脳{10}^{-6}\text{m}脳\sin \left(-65\right)\right|}{3} \\ 位=0.523脳{10}^{-6}\text{m} \\ 位=\text{523}\text{nm} \end{gathered}$$

The average of the wavelengths to calculate the best wavelength,

$$\begin{gathered} 位=\frac{523\text{nm}+524\text{nm}+522\text{nm}+523\text{nm}+523\text{nm}}{5} \\ 位=523\text{nm} \end{gathered}$$

Hence the best fit wavelength is, 523 nm.