$\frac{\Delta a }{ a } \times 100=1 \%,$$ \frac{\Delta b }{ b } \times 100=3 \%,$$ \frac{\Delta c }{ c } \times 100=2 \%$ and $\frac{\Delta d }{ d } \times 100=2 \%$
$\frac{\Delta A }{ A } \times 100=2 \frac{\Delta a }{ a } \times 100+3 \frac{\Delta b }{ b } \times 100+$$\frac{\Delta c }{ c } \times 100+\frac{1}{2} \times \frac{\Delta d }{ d } \times 100$
$\frac{\Delta A }{ A } \times 100=2 \times 1+3 \times 3+2+\frac{1}{2} \times 2=14 \%$
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Which of the following statement($s$) is (are) correct?
$(A)$ The phase difference between the two rays is independent of $d$.
$(B)$ The two rays interfere constructively at the detector.
$(C)$ The phase difference between the two rays depends on $n _1$ but is independent of $n_2$.
$(D)$ The phase difference between the two rays vanishes only for certain values of $d$ and the angle of incidence of the beam, with $\theta$ being the corresponding angle of refraction.