91影视

Angle for first-order maximum $\left({胃}_1\right)$is $11.3掳$.

A set of a large number of parallel slits of equal width and which are equidistant between the centers is known as grating.The angular position of the fringe is given by the following relation.

$\mathit{s}\mathit{i}\mathit{n}{\mathit{胃}}_{\mathbf{m}}\mathbf{=}\frac{\mathbf{m}\mathbf{位}}{\mathbf{d}}$

Here, $\mathit{位}$ is the wavelength of light used and is the slit width.

Given:${胃}_1=11.3^{鈭�}$

Now, the angular position of the bright fringes is given by

$sin{胃}_m=\frac{m位}{d}$

Whereas $m=0,卤1,卤2,...$

The first-order maximum is for$m=卤1$

Hence,

$sin{胃}_1=\frac{位}{d}鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�\left(1\right)$

And the fourth-maximum is for

$\sin {胃}_4=\frac{4位}{d}鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�鈰�\left(1\right)$

Divide (2) by (1),

$$\begin{gathered} \sin {胃}_4=4sin{胃}_1 \\ {胃}_4={\sin }^{-1}\left(4\sin {胃}_1\right) \\ ={\sin }^{-1}\left(4\sin 11.3掳\right) \\ =51.6掳 \end{gathered}$$

Thus, the angular position of the fourth-order maximum is $51.6掳$.