91影视

Grating lines on the diffraction grating are 10000 liner per cm, which means that the $d=\left(\frac{1cm}{10000}\right)\left(\frac{1m}{100cm}\right)=1脳{10}^{鈥�6}m$

distance between the two slits is

The order of maximum is 1.

The angles at which the first-order maximum is observed ${}^{\mathbf{24}\mathbf{.}{\mathbf{2}}^{\mathbf{鈭�}}\mathbf{,}\mathbf{25}\mathbf{.}{\mathbf{7}}^{\mathbf{鈭�}}\mathbf{,}\mathbf{29}\mathbf{.}{\mathbf{1}}^{\mathbf{鈭�}}\mathbf{,}\mathbf{and}\mathbf{}\mathbf{41}\mathbf{.}{\mathbf{0}}^{\mathbf{鈭�}}}$

The equation of the constructive interference can be expressed as

$\mathbf{d}\mathbf{}\mathbf{蝉颈苍胃}\mathbf{}\mathbf{=}\mathbf{尘位}$ 鈥︹赌︹赌︹赌︹赌︹赌︹赌�(1)

Where, d, $位,胃$and m is the separation between slits, the wavelength of the incident light, and the angle made with the maximum and order of maximum, respectively.

Therefore, if we substitute ${}^{\mathbf{胃}\mathbf{=}\mathbf{24}\mathbf{.}{\mathbf{2}}^{\mathbf{鈭�}}}$and m=1 in equation (1), we will get,

$$\begin{gathered} 位=\frac{\mathrm{d蝉颈苍胃}}{\mathrm{m}} \\ =\frac{\left(1.0脳{10}^{鈥�6}\mathrm{m}\right)脳\sin \left(24.2^{鈭�}\right)}{1} \\ =\left(4.1脳{10}^{鈥�7}\mathrm{m}\right)\left(\frac{1\mathrm{nm}}{{10}^{鈥�9}\mathrm{m}}\right) \\ =410\mathrm{nm} \end{gathered}$$

For $胃=25.7^{鈭�}$and m=1, the equation (1) will result,

$$\begin{gathered} 位=\frac{\mathrm{d蝉颈苍胃}}{\mathrm{m}} \\ =\frac{\left(1.0脳{10}^{鈥�6}\mathrm{m}\right)脳\sin \left(25.7^{鈭�}\right)}{1} \\ =\left(4.34脳{10}^{鈥�7}\mathrm{m}\right)\left(\frac{1\mathrm{nm}}{{10}^{鈥�9}\mathrm{m}}\right) \end{gathered}$$

$=434\mathrm{nm}$

For $\mathrm{胃}=29.1^{鈭�}$and m=1, the equation (1) will result,

$$\begin{gathered} 位=\frac{\mathrm{d蝉颈苍胃}}{\mathrm{m}} \\ =\frac{\left(1.0脳{10}^{鈥�6}\mathrm{m}\right)脳\sin \left(29.1^{鈭�}\right)}{1} \\ =\left(4.86脳{10}^{鈥�7}\mathrm{m}\right)\left(\frac{1\mathrm{nm}}{{10}^{鈥�9}\mathrm{m}}\right) \\ =486\mathrm{nm} \end{gathered}$$

For $\mathrm{胃}=41.0^{鈭�}$and m=1, the equation (1) will result,

$$\begin{gathered} 位=\frac{\mathrm{d蝉颈苍胃}}{\mathrm{m}} \\ =\frac{\left(1.0脳{10}^{鈥�6}\mathrm{m}\right)脳\sin \left(29.1^{鈭�}\right)}{1} \\ =\left(6.56脳{10}^{鈥�7}\mathrm{m}\right)\left(\frac{1\mathrm{nm}}{{10}^{鈥�9}\mathrm{m}}\right) \\ =656\mathrm{nm} \end{gathered}$$

Therefore, the wavelengths for the first-order maximum observed at angles are.${}^{24.2^{鈭�},25.7^{鈭�},29.1^{鈭�},\mathrm{and}41.0^{鈭�}\mathrm{are}434\mathrm{nm},486\mathrm{nm},656\mathrm{nm}.}$