Answer
$\theta_1 = 1.6^{\circ}$
$\theta_2 = 3.2^{\circ}$
Work Step by Step
We can find the distance between each pair of adjacent slits:
$d = \frac{4.0~cm}{2000} = 2.0\times 10^{-5}~m$
We can write an expression for the angles of the diffraction orders:
$sin~\theta_m = \frac{m~\lambda}{d}$
We can find the angle of the first diffraction order:
$sin~\theta_1 = \frac{(1)~\lambda}{d}$
$sin~\theta_1 = \frac{550\times 10^{-9}~m}{2.0\times 10^{-5}~m}$
$sin~\theta_1 = 2.75\times 10^{-2}$
$\theta_1 = sin^{-1}~(2.75\times 10^{-2})$
$\theta_1 = 1.6^{\circ}$
We can find the angle of the second diffraction order:
$sin~\theta_2 = \frac{(2)~\lambda}{d}$
$sin~\theta_2 = \frac{(2)(550\times 10^{-9}~m)}{2.0\times 10^{-5}~m}$
$sin~\theta_2 = 5.50\times 10^{-2}$
$\theta_2 = sin^{-1}~(5.50\times 10^{-2})$
$\theta_2 = 3.2^{\circ}$
