Answer
a) decreased slit separation
b) $d=5.64\times 10^{-5}m$
Work Step by Step
(a) We know that $sin\theta \frac{1}{d}$ . This relationship shows that $\theta$ and $d$ are inversely proportional. So, when $\theta$ increases the value of $sin\theta$ increases and as a result, the value of $d$ decreases and we have decreased slit separation.
(b) We know that
$\theta=tan^{-1}(\frac{y}{L})$
$\theta=tan^{-1}(\frac{0.18m}{2.3m})=4.47^{\circ}$
Now $d=\frac{m\lambda}{sin\theta}$
We plug in the known values to obtain:
$d=\frac{(10)(440\times 10^{-9}m)}{sin 4.47^{\circ}}$
$d=5.64\times 10^{-5}m$
