91影视

The given data is listed below as-

• The width of the diffraction grating is 20.0 mm.
• The number of rulings = 6000.
• The wavelength of light, $位=589\text{nm}$ .

The condition of the diffraction grating is:

$dsin胃=m位$

Here, d is the distance between adjacent rulings and $位$ is the wavelength of light.

The distance between adjacent rulings is:

$$\begin{gathered} d=20.006000 \\ =0.00333mm \\ =3.33渭m \end{gathered}$$

Now, the condition of the diffraction grating is:

$d\sin 胃=m位$

Where, $m=0,卤1,卤2,....$

Now, the largest value of $胃$corresponds to $\left|m\right|=5$.

Therefore, the value of $胃$is:

$\begin{array}{l}胃={\sin }^{-1}\left(\left|m\right|\raisebox{1ex}{$位$}\!\left/ \!\raisebox{-1ex}{$d$}\right.\right)\\ ={\sin }^{-1}\left(\frac{5(0.589)渭m)}{3.33渭\mathrm{m}}\right)\\ =62.1^0\end{array}$

Thus,the largest value of$胃$at which maxima appear on a distant viewing screen is $62.1掳$.

The second largest value of $胃$corresponds to $\left|m\right|=4$.

Therefore, the value of $胃$is:

$\begin{array}{l}胃={\sin }^{-1}\left(\left|m\right|\raisebox{1ex}{$位$}\!\left/ \!\raisebox{-1ex}{$d$}\right.\right)\\ ={\sin }^{-1}\left(\frac{4(0.589)渭m)}{3.33渭\mathrm{m}}\right)\\ =45.0^{鈭�}\end{array}$

Thus,the second largest value of $胃$ at which maxima appear on a distant viewing screen is $45.0掳$.

The third largest value of $胃$ corresponds to$\left|m\right|=3$ .

Therefore, the value of $胃$ is:

role="math" localid="1663159335558" $\begin{array}{l}胃={\sin }^{-1}\left(\left|m\right|\raisebox{1ex}{$位$}\!\left/ \!\raisebox{-1ex}{$d$}\right.\right)\\ ={\sin }^{-1}\left(\frac{3(0.589)渭m)}{3.33渭\mathrm{m}}\right)\\ =32.0^{鈭�}\end{array}$

Thus, the third largest value of $胃$ at which maxima appear on a distant viewing screen is $32掳$.