91影视

The given data is listed below as-

The wavelength of light,$位=600\text{nm}$

The width of silts is 300 mm

The separation of silts,$d=900\text{nm}$

The number of silts is $N=1000$.

The condition of the diffraction grating is:

$dsin胃=m位$

Here, d is the distance between adjacent rulings, m is an integer and $位$ is the wavelength of light.

To find the greatest value of m for the maxima, the equation is given by 鈥�

$d\sin 胃=m位<d$

Therefore,

$$\begin{gathered} m<\frac{d}{位} \\ m<\frac{900\text{nm}}{600\text{nm}}=1.5 \end{gathered}$$

So, $m=1$.

Thus, there are three maxima that can be seen in the full diffraction pattern having $m=0,卤1$.

The half-width of the lines is given by 鈥�
$$\begin{gathered} 螖{胃}_{hw}=\frac{位}{Nd\cos 胃} \\ =\frac{d\sin 胃}{Nd\cos 胃} \\ =\frac{\tan 胃}{N} \\ =\frac{1}{N}\tan \left[{\sin }^{-1}\left(\frac{位}{d}\right)\right] \end{gathered}$$

Substitute all the value in the above equation. For $N=1000$, $位=600\text{nm}$ and $d=900\text{nm}$.

role="math" localid="1663310103256" $$\begin{gathered} 螖{胃}_{hw}=\frac{1}{1000}\tan \left[{\sin }^{-1}\left(\frac{600\text{nm}}{900\text{nm}}\right)\right] \\ =8.944脳{10}^{-4}\text{rad} \\ =8.944脳{10}^{-4}\text{rad}脳\left(\frac{{180}^0}{蟺\text{rad}}\right) \\ =0.051掳 \end{gathered}$$

Thus,the angular width of a spectral line observed in the first order is $0.051掳$.