91Ó°ÊÓ

The wavelength of the spectrum $\mathrm{λ}=700n\mathrm{m}$.

Diffraction grating,$\frac{W}{N}=\frac{1}{5\mathrm{li}ne/\mathrm{mm}}$

The expression for the maxima of the diffraction grating is given as follows.

$\mathit{d}\mathit{s}\mathit{i}\mathit{n}\mathit{θ}\mathbf{=}\mathit{m}\mathit{λ}$ …… (i)

Here, $\mathit{d}$is the slit separation, $\mathit{m}$is the order of the diffraction,$\mathit{λ}$ is the wavelength and $\mathit{θ}$is the angle.

The value of angle for which entire spectrum would exist is ${90}^{°}$and wavelength is$700nm$ .

Calculate the slit separation,

role="math" localid="1663138744202" $\begin{array}{l}d=\frac{w}{N}\\ d=\frac{1}{500x{10}^{3}line/m}\\ d=2×{10}^{-6}m\end{array}$

Substitute the values and solve as:

$\begin{array}{l}d=\frac{1}{500x{10}^{3}line/m}\\ d=2×{10}^{-6}m\end{array}$

Calculate the order of the entire visible spectrum.

Substitute $700nm$for $\mathrm{λ}$, ${90}^{°}$for$\mathrm{θ}$ and$2×{10}^{-6}$ for $d$into equation (i).

$$\begin{gathered} 2×{10}^{-6}×\sin {90}^{°}=m×700×{10}^{-9} \\ m=\frac{2×{10}^{-6}×\sin {90}^{°}}{700×{10}^{-9}} \\ m=\frac{2×{10}^{-6}}{7×{10}^{-7}} \\ m=2.876 \end{gathered}$$

Hence the maximum order for which full spectrum is exit is $2$.