91Ó°ÊÓ

The wavelength of the light is $\mathrm{λ}=610\text{nm}$.

The angle on vertical axis is ${\mathrm{Î\pm }}_s=12\text{rad}$.

The angle of the diffraction is defined as the angle of central axis from the diffraction minima of different orders.

(a)

The slit width is given as:

${\mathrm{Î\pm }}_s=\frac{\mathrm{Ï€}d}{\mathrm{λ}}$

Substitute all the values in equation.

$$\begin{gathered} 12\text{rad}=\frac{\mathrm{Ï€}d}{610\text{nm}} \\ d=2330.03\text{nm} \end{gathered}$$

Therefore, the slit width is $2330.03\text{nm}$.

(b)

The total number of diffraction minima in diffraction pattern is given as:

$m\mathrm{λ}=d\sin \mathrm{θ}$

Here, $\mathrm{θ}$is diffraction angle and its value for total number of minima is $90°$. because beyond this angle diffraction is not observed.

Substitute all the values in equation.

$$\begin{gathered} m\left(610\text{nm}\right)=\left(2330.03\text{nm}\right)\left(\sin 90°\right) \\ m=3.82 \\ m≈4 \end{gathered}$$

Therefore, the total number of diffraction minima in diffraction pattern is $4$.

(c)

The least angle for minimum is given as:

$\sin {\mathrm{θ}}_{\min }=\frac{m\mathrm{λ}}{d}$

The value of m is 1 for least angle for minimum.

Substitute all the values in equation.

$$\begin{gathered} \sin {\mathrm{θ}}_m=\frac{\left(1\right)\left(610\text{nm}\right)}{2330.03\text{nm}} \\ {\mathrm{θ}}_{\min }=15.2° \end{gathered}$$

Therefore, the least angle for minimum is $15.2°$.

(d)

The greatest angle for minimum is given as:

$\sin {\mathrm{θ}}_{\max }=\frac{m\mathrm{λ}}{d}$

The value of m is 3 for greatest angle for minimum.

Substitute all the values in equation.

$$\begin{gathered} \sin {\mathrm{θ}}_{\max }=\frac{\left(3\right)\left(610\text{nm}\right)}{2330.03\text{nm}} \\ {\mathrm{θ}}_{\max }=51.2° \end{gathered}$$

Therefore, the greatest angle for minimum is $51.2°$.