91影视

The diffraction grating is made of equally spaced parallel lines, which can be considered as a slit. The lightwave when passes through these parallel slits result in interference patterns of different orders.

The number of slits is inversely proportional to the slit separation, of the value $\mathbf{d}$. So, for the sake of getting the maximum number of lines per centimeter, we are supposed to minimize the value $\mathbf{d}$. The equation of the constructive interference:

$\mathbf{胃蝉颈苍位}$ reveals that the smaller the value $\mathbf{d}$, the smaller will be $\mathbf{位}$.

Then, to produce a complete first-order spectrum for visible light, we are supposed to evaluate the minimum $\mathrm{位}$has to belocalid="1654054017267" $780\mathrm{nm}$.

The value must be localid="1654054020898" $\mathrm{m}=1,\mathrm{and}90.0^{掳}\mathrm{in}\mathrm{胃蝉颈苍位}$, and we get,

localid="1654245378786" $$\begin{gathered} \mathrm{d}=\frac{\mathrm{尘位}}{\mathrm{蝉颈苍胃}} \\ =\frac{1脳780脳{10}^{鈥�9}\mathrm{m}}{\sin \left(90.0^{掳}\right)} \\ =7.8脳{10}^{鈥�7} \end{gathered}$$

The number of lines per cm is then evaluated as:

$$\begin{gathered} \mathrm{n}=\frac{1\mathrm{cm}}{\mathrm{d}} \\ =\left(\frac{1\mathrm{cm}}{7.8脳{10}^{鈥�7}\mathrm{m}}\right)\left(\frac{1\mathrm{m}}{100\mathrm{cm}}\right) \\ =1.28脳{10}^4 \end{gathered}$$

Therefore, the maximum number of lines is $1.28脳{10}^4$lines per centimeter.