Calculate the angle of the second-order maximum for monochromatic light of wavelength 550nm if it illuminates
a)a double slit with a slit seperation of 2.0x10^-6m
b)a diffraction grating with 10 500 slits in 1.0m
2nd fringe occurs when m = 2:
$\displaystyle d\sin \theta = m\lambda$
$\displaystyle \left(2.0 \cdot 10^{-6}m\right) \sin \theta = (2)\left(5.5 \cdot 10^{-7} m \right)$
Solve for $\displaystyle \theta$.
For multiple-slit interference with diffraction gratings, we have the same equation as above also with m = 2:
$\displaystyle d\sin \theta = m\lambda$
To find d, note that each slit are presumed to be equally spaced from one another. So, the distance between two slits is:
$\displaystyle d = \frac{1.0 m}{10500} = 9.5238 \cdot 10^{-5} m$