(a) (i) (1) What are coherent sources? Why are they necessary for observing a sustained interference pattern? (2) Lights from two independent sources…

a)

i) $\displaystyle 1$) If the phase difference between the displacement produced by each of the wave from two sources does not change with time then two sources are said to be coherent. Alternatively Two sources are said to be coherent if they emit light continuously of same frequency / wavelength and having zero or constant phase difference. Coherent sources are required to get constant phase difference. $\displaystyle 2$) Two independent sources will never be coherent because phase difference between them will not be constant.

ii) $\displaystyle 1$) Distance between adjacent bright fringe = fringe width \[\beta=\frac{\lambda D}{d} \] \[=\frac{600 \times 10^{-9} \times 1.2}{0.1 \times 10^{-3}}=7.2 \mathrm{~mm} \]

2) \[\begin{aligned} \theta & =\frac{\lambda}{d} \\ & =\frac{600 \times 10^{-9}}{0.1 \times 10^{-3}}=6 \times 10^{-3} \mathrm{rad}=0.34^{\circ} \end{aligned} \]