Answer
a) $\theta_1=18^o$; $\theta_2=39^o$; $\theta_3=70^o$
b) $\theta_1=39^o$
c) no solution
Work Step by Step
$D\sin(\theta)=m\lambda$
$\theta=\arcsin(\frac{m\lambda}{D})$
a) $\theta_1=\arcsin(\frac{1(0.50cm)}{1.6cm})=18^o$
$\theta_2=\arcsin(\frac{2(0.50cm)}{1.6cm})=39^o$
$\theta_3=\arcsin(\frac{3(0.50cm)}{1.6cm})=70^o$
$\theta_4=\arcsin(\frac{4(0.50cm)}{1.6cm})=$ no solution
b) $\theta_1=\arcsin(\frac{1(1.0cm)}{1.6cm})=39^o$
$\theta_2=\arcsin(\frac{2(1.0cm)}{1.6cm})=$ no solution
c) $\theta_1=\arcsin(\frac{1(3.0cm)}{1.6cm})=$ no solution