(Solved): example as a substitution \( \delta=d \sin \theta \) problem. Calculate the slit separation as the ...

example as a substitution \( \delta=d \sin \theta \) problem. Calculate the slit separation as the inverse \( \quad d=1 / 6,300 \mathrm{~cm}=1.587 \times 10^{-4} \mathrm{~cm}=1,587 \mathrm{~nm} \) of the number of grooves per centimeter: Solve for \( \sin \theta \) and substitute numerical values for the first-order maximum \( (m=1) \) to find \( \theta_{1} \) : \[ \begin{array}{l} \sin \theta_{1}=\frac{(1) \lambda}{d}=\frac{632.8 \mathrm{~nm}}{1,587 \mathrm{~nm}}=0.3987 \\ \theta_{1}= \\ \end{array} \] Repeat for the second-order maximum \[ (m=2) \] \[ \begin{array}{l} \sin \theta_{2}=\frac{(2) \lambda}{d}=\frac{2(632.8 \mathrm{~nm})}{1,587 \mathrm{~nm}}=0.7973 \\ \theta_{2}= \\ \end{array} \] HINTS: GETTING STARTED I I'M STUCK! Suppose light with wavelength \( 8.00 \times 10^{2} \mathrm{~nm} \) is used instead and the diffraction grating has \( 3.10 \times 10^{3} \) lines per centimeter. Find the angles of all the principal maxima. (Enter NONE in any unused boxes.) \[ \begin{array}{ll} \theta_{0}= & 0 \\ \theta_{1}= & \circ \\ \theta_{2}= & \circ \\ \theta_{3}= & \circ \end{array} \]