Question

Show that a grating with 103 grooves/cm provides a dispersion of 5.88 per mm of wavelength if n 5 1 and f 5 108 in Equation 20-4.

Short answer

$0.102radians/\mu m.\frac{180°}{\mathrm{\pi radians}}=5.8°/\mu m$

Step-by-step solution

Step: 1 Define grating:

Diffraction grating is a series of clusters used to separate an incident wave into its wavelength by directly separating the magnitude of the diffraction.

Step: 2 Calculating the dispersion of wavelength:

The ${10}^3$ grooves/cm is:

$d={10}^{-5}m=10\mu m$

Dispersion is:

$$\begin{gathered} \frac{n}{d.\cos \left(\varphi \right)}=\frac{1}{10.\cos \left(10°\right)}=0.102radians/\mu m \\ 0.102radians/\mu m.\frac{180°}{\mathrm{\pi }\mathrm{radians}}=5.8°/\mu m \end{gathered}$$

The solution is $0.102radians/\mu m.\frac{180°}{\mathrm{\pi }\mathrm{radians}}=5.8°/\mu m$