91影视

If the incident angle of the wave $\left(\mathbf{胃}\right)$, measured from the surfaces of the reflecting plane and the radiation's wavelength $\left(\mathbf{位}\right)$, fulfil Bragg's equation, diffraction maxima (caused by constructive interference) is achieved. The Bragg鈥檚 equation is given as-

$\mathbf{2}\mathbf{诲蝉颈苍胃}\mathbf{=}\mathbf{尘位}\left(\mathbf{m}\mathbf{=}\mathbf{1}\mathbf{,}\mathbf{2}\mathbf{,}\mathbf{3}...\right)$

Where$\mathbf{d}$is the interplanar distance and is the order of the maximum intensity.

The wavelength of light used: $位=0.125\text{nm}$

Plane separation: $d=0.252\text{nm}$

Angle of incidence: $胃=45掳$

If the crystal is rotated by an angle $蠒$, the new angle of incident is$胃卤蠒$ depending on the clockwise or counter-clockwise rotation.

Using the values given in the question,

For $m=1$, in clockwise direction, the angle $胃-蠒$is

role="math" localid="1663051508257" $$\begin{gathered} 胃-蠒={\sin }^{-1}\frac{m位}{2d} \\ 45掳-蠒={\sin }^{-1}\frac{\left(0.125nm\right)\left(1\right)}{2\left(0.252nm\right)} \\ 蠒=45掳-{\sin }^{-1}0.248 \\ 蠒=30.64掳 \end{gathered}$$

For $m=2$, in clockwise direction, the angle $胃-蠒$is

$$\begin{gathered} 胃-蠒={\sin }^{-1}\frac{m位}{2d} \\ 45掳-蠒={\sin }^{-1}\frac{\left(0.125nm\right)\left(2\right)}{2\left(0.252nm\right)} \\ 蠒=45掳-{\sin }^{-1}0.496 \\ =15.26掳 \end{gathered}$$

For $m=3$, in counter-clockwise direction, the angle $胃+蠒$is

$$\begin{gathered} 胃+蠒={\sin }^{-1}\frac{m位}{2d} \\ 45掳+蠒={\sin }^{-1}\frac{\left(0.125nm\right)\left(3\right)}{2\left(0.252nm\right)} \\ 蠒={\sin }^{-1}0.744-45掳 \\ =3.1掳 \end{gathered}$$

For $m=4$, in counter-clockwise direction, the angle $胃+蠒$is

$$\begin{gathered} 胃+蠒={\sin }^{-1}\frac{m位}{2d} \\ 45掳+蠒={\sin }^{-1}\frac{\left(0.125nm\right)\left(4\right)}{2\left(0.252nm\right)} \\ 蠒={\sin }^{-1}0.992-45掳 \\ =37.8掳 \end{gathered}$$

The smaller and larger values of$蠒$ for clockwise rotation are$蠒=15.26掳$ and$蠒=30.64掳$ respectively. The smaller and larger values of$蠒$ for counter-clockwise rotation are$蠒=3.1掳$ and$蠒=37.8掳$ respectively.