(1)  $∆$x = d sin α

= dα (as α is very small) $\mathrm{\alpha }=\frac{0.36}{180}$ = (2 × 10^–3) rad

$\frac{\mathrm{\Delta x}}{\mathrm{\lambda }}=\frac{(3\times {10}^{-4})(2\times {10}^{-3})}{6\times {10}^{-7}}=1$

So constructive interference

(2)  $\mathrm{\beta }=\frac{\mathrm{D\lambda }}{\mathrm{d}}$

(3)  ${\mathrm{\Delta x}}_{\mathrm{p}}=\mathrm{d\alpha }+\frac{\mathrm{dy}}{\mathrm{D}}$ 

            = 3 × 10^–4 (2 × 10^–3 + 11 × 10^–3)

            = 39 × 10^–7

$\frac{{\mathrm{\Delta x}}_{\mathrm{p}}}{\mathrm{\lambda }}=\frac{39\times {10}^{-7}}{6\times {10}^{-7}}$ = 6.5 so destructive

(4) ${\mathrm{\Delta x}}_{\mathrm{p}}=\frac{\mathrm{dy}}{\mathrm{D}}$ = (3 × 10^–4) × 11 × 10^–3

            = 33 × 10^–7

$\frac{{\mathrm{\Delta x}}_{\mathrm{p}}}{\mathrm{\lambda }}=\frac{33\times {10}^{-7}}{6\times {10}^{-7}}$= 5.5 ⇒ destructive