91影视

The expression for the slit width of the diffraction grating is given by,

$$\begin{gathered} \mathit{尾}\mathbf{=}\frac{\mathbf{蟺}\mathbf{d}}{\mathbf{位}}\mathit{s}\mathit{i}\mathit{n}\mathit{胃} \\ \mathit{d}\mathbf{=}\mathbf{\left(}\frac{\mathbf{尾}}{\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{胃}}\mathbf{\right)}\mathbf{\left(}\frac{\mathbf{位}}{\mathbf{蟺}}\mathbf{\right)} \end{gathered}$$ 鈥︹�� (1)

Here, d is slit separation,$\mathit{尾}$is slit width,$\mathit{位}$is wavelength, and$\mathit{胃}$is angle of diffraction.

From the graph, the ratio of slit with to sine of angle is,

$\begin{array}{rcl}\frac{尾}{\sin 胃}& =& \frac{80\text{rad}}{1}\\ & =& 80\text{rad}\end{array}$

Substitute$80\text{rad}$for $\frac{尾}{\sin 胃}$, and$435脳{10}^{-9}\text{m}$for in equation (1).

$\begin{array}{rcl}d& =& \left(80\text{rad}\right)\left(\frac{435脳{10}^{-9}\text{m}}{蟺}\right)\\ & =& 11.1脳{10}^{-6}\text{m}\\ & =& 11.1渭m\end{array}$

Therefore, the slit separation is$11.1渭m$.

The condition for the constructive interference maxima is given by,

$\begin{array}{rcl}d\sin {胃}_{\max }& =& m_{\max }位\\ m_{\max }& =& \frac{d\sin {胃}_{\max }}{位}\end{array}$ 鈥︹�� (2)

Here,${胃}_{\max }$is the maximum angle, and$m_{\max }$is the number of maxima.

Substitute $11.1脳{10}^{-6}\text{m}$for$d$,$90掳$for ${胃}_{\max }$, and$435脳{10}^{-9}\text{m}$for$位$in equation (2).

$\begin{array}{rcl}{m}_{\max }& =& \frac{\left(11.1脳{10}^{-6}\text{m}\right)\sin 90掳}{435脳{10}^{-9}\text{m}}\\ & =& 25.52\\ & 鈮�& 25\end{array}$

The number of interference maxima are 25 and the central maxima is formed at 0 . So, the number of interference minima are 25 .

The total number of interference maxima and minima on both sides of the interference pattern is,

$$\begin{gathered} n=25+25 \\ =50 \end{gathered}$$

Therefore, the total number of interference maxima on both sides of the interference pattern is 50.

The least maxima is occurred at the center if the interference pattern.

$m_{\max }=0$

From equation (1),

$$\begin{gathered} {胃}_{\max }={\sin }^{-1}\left(\frac{m_{\max }位}{d}\right) \\ ={\sin }^{-1}\left(\frac{\left(0\right)位}{d}\right) \\ =0掳 \end{gathered}$$

Therefore, the smallest angle for maxima is$0掳$ .

The number of minima is 25. So, the smallest minima is occurred at 1 and the greatest minima is occurred at 25 .

$m_{\min }=25$

The condition for interference minima is given by,

$$\begin{gathered} d\sin {胃}_{\min }=m_{\min }位 \\ {胃}_{\min }={\sin }^{-1}\left(\frac{m_{\min }位}{d}\right) \end{gathered}$$ 鈥︹�� (3)

Substitute$11.1脳{10}^{-6}\text{m}$ for$d$ ,$25$ for$m_{\min }$ , and$435脳{10}^{-9}\text{m}$ for$位$ in equation (3).

$$\begin{gathered} {胃}_{\min }={\sin }^{-1}\left(\frac{\left(25\right)\left(435脳{10}^{-9}\text{m}\right)}{11.1脳{10}^{-6}\text{m}}\right) \\ =78.44掳 \end{gathered}$$

Therefore, the greatest angle for minima is$78.44掳$ .