Answer
$3.4^{\circ}$
Work Step by Step
We can find the required angle as follows:
$\theta_r=sin^{-1}(mN\lambda_r)$
We plug in the known values to obtain:
$\theta_r=(1)(22\times 10^4m^{-1})(680\times 10^{-9}m)$
$\theta_r=8.60^{\circ}$
and $\theta_b=sin^{-1}(mN\lambda_b)$
We plug in the known values to obtain:
$\theta_b=sin^{-1}(1)(22\times 10^4m^{-1})(410\times 10^{-9}m)$
$\theta_b=5.17^{\circ}$
Now $\theta=\theta_r-\theta_b$
$\implies \theta=8.60^{\circ}-5.17^{\circ}=3.4^{\circ}$
