Answer
(a) $\theta_{2}$ = 18.75$^{\circ}$
Work Step by Step
For this problem, we use the following information:
$\frac{c_{1}}{c_{2}}$ = $\frac{\sin θ_{1}}{\sin θ_{2}}$
$c_{1}$ = 3 x $10^{8}$ $\frac{m}{s}$
Now, we want to express the equation in terms of $\theta_{2}$.
1. $\sin θ_{2} \times (\frac{c_{1}}{c_{2}})$ = $\sin θ_{1}$
2. $\sin θ_{2}$ = $\sin θ_{1}$ $\times$ $(\frac{c_{2}}{c_{1}})$
3. $\theta_{2}$ = $\sin^{-1}$( [$\sin θ_{1}$ $\times$ $(\frac{c_{2}}{c_{1}})$] )
From here, we can plug in the values to solve for $\theta_{2}$.
(a) $\theta_1$ = 40$^{\circ}$ $c_2$ = 1.5 x $10^8$ $\frac{m}{s}$
$\theta_{2}$ = $\sin^{-1}$( [$\sin 40^{\circ}$ $\times$ $(\frac{1.5 x 10^8}{3 x 10^{8}})$] )
$\theta_{2}$ = 18.75$^{\circ}$
