91影视

Grating lines on the reflection grating have a separation of $\mathrm{d}=\left(8\mathrm{渭尘}\right)\left(\frac{{10}^{鈥�6}\mathrm{m}}{1\mathrm{渭尘}}\right)=8.0脳{10}^{鈥�6}鈥�\mathrm{m}$

The wavelength of the red color light is ${位}_{\mathrm{red}}=700\mathrm{nm}\left(\frac{{10}^{鈥�9}\mathrm{m}}{1\mathrm{渭尘}}\right)=7脳{10}^{鈥�7}鈥�\mathrm{m}$

The wavelength of the blue color light is ${\mathrm{位}}_{\mathrm{blue}}=470\mathrm{nm}\left(\frac{{10}^{鈥�9}\mathrm{m}}{1\mathrm{渭尘}}\right)=4.7脳{10}^{鈥�7}鈥�\mathrm{m}$

The equation of the constructive interference can be expressed as

$\mathbf{胃}\mathbf{}\mathbf{蝉颈苍位}$ 鈥︹赌︹赌︹赌︹赌︹赌︹赌�(1)

Where, d, $\mathrm{位}$, $\mathrm{胃}$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.

For a given value of $\mathrm{位}$we can determine the angle for the first-order maximum (m=1) using the formula using equation (1),

$\mathrm{胃}={\sin }^{鈥�1}\left(\frac{\mathrm{位}}{\mathrm{d}}\right)$role="math" localid="1654063410339" ${}_{.......................\left(2\right)}$

(a)

Therefore, using equation (2) for the red color light will give the maximum at an angle of,

$$\begin{gathered} {\mathrm{胃}}_{Red}={\sin }^{鈥�1}\left(\frac{7脳{10}^{鈥�7}\mathrm{m}}{8.0脳{10}^{鈥�6}\mathrm{m}}\right) \\ ={\sin }^{鈥�1}\left(0.0875\right) \\ =5.02掳 \end{gathered}$$

Therefore, for the red color, the first-order maximum will be observed at an angle of $5.02掳$.

(b)

Therefore, using equation (2) for the blue color light will give the maximum at an angle of,

$$\begin{gathered} {\mathrm{胃}}_{Red}={\sin }^{鈥�1}\left(\frac{4.7脳{10}^{鈥�7}\mathrm{m}}{8.0脳{10}^{鈥�6}\mathrm{m}}\right) \\ ={\sin }^{鈥�1}\left(0.0875\right) \\ =3.37掳 \end{gathered}$$

Therefore, for the blue color, the first-order maximum will be observed at an angle of $3.37掳$.