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  4. A YDSE is performed with bi-chromatic light (5500 mathringA and 6000 mathringA) for d=2 mm and D=1 m. Distance of first complete maxima from the central maxima on the screen, is

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Q. A YDSE is performed with bi-chromatic light $(5500\,\mathring{A}$ and $6000 \,\mathring{A})$ for $d=2\, mm$ and $D=1\, m$. Distance of first complete maxima from the central maxima on the screen, is

Solution:

$y=\frac{n_{1} \lambda_{1} D}{d}=\frac{n_{2} \lambda_{2} D}{d}$
$\frac{n_{1}}{n_{2}}=\frac{\lambda_{2}}{\lambda_{1}}=\frac{12}{11}$
$n_{1}=12$
$y=\frac{12 \times 5500 \times 10 \times 1}{2 \times 10^{-3}}$
$=330 \times 10^{-5}=3.3 \,mm$