91影视

In diffraction grating, the condition to achieve maxima is given as-

$\mathrm{诲蝉颈苍胃}=\mathrm{尘位}$.

Here, is the separation between grating lines, $\mathrm{胃}$is the angle made with the normal by the diffracted ray, $\mathrm{m}$ is the order of diffraction and $\mathrm{位}$ is the wavelength.

• Wavelength of the sodium doublet is $589.00\text{nmand}589.59\text{nm}$.
• Angle to the normal is$10掳$ .

(a)

Here, the sodium doublet is viewed in the third order at$胃=10掳$ . So,$m=2$ .

Now, the grating spacing can be obtained as follows:

$d=\frac{m{位}_{avg}}{\sin 胃}$

For the given values, the above equation becomes-

$d=\frac{m\left(\frac{589.00+589.59}{2}\right)}{\sin 10掳}$

$=\frac{3\left(\frac{589.00\text{nm}+589.59\text{nm}}{2}\right)}{\sin 10掳}$

$=1.0脳{10}^4鈥�\text{nm}$

$=10渭m$

Thus, the grating spacing is$10渭m$ .

(b)

The width of the ruling $\left(L\right)$can be obtained as the product of the number of rulings $\left(N\right)$and the grating width . The relation can be written as-

$L=N脳d路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路路\left(1\right)$

The number of rulings on the grating is given as-

$N=\frac{{位}_{avg}}{m螖位}$

Here, ${位}_{avg}$is the average wavelength of the doublet and$螖位$ is the wavelength separation.

So, the total length $\left(L\right)$ becomes-

$L=\frac{d{位}_{avg}}{m螖位}$

For the given values, the above equation becomes-

$L=\frac{\left(10脳{10}^{-6}\right)\text{m}脳\left(\frac{589.00\text{nm}+589.59\text{nm}}{2}\right)}{3脳\left(589.59\text{nm}-589.00\text{nm}\right)}$

role="math" localid="1663060959560" $=3.3脳{10}^3渭m$

$=3.3mm$

Thus, the total width of the rulings is $3.3mm$.