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YDSE Problems II

In an interfe...

Question

In an interference pattern the $(n + 4)^{t h}$ blue bright fringe and $n^{t h}$ red bright fringe are formed at the same spot. If red and blue light have the wavelength of $7800 Å$ and $5200 Å$ , then value of $n$ should be :

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Solution

Fringes are formed at same spot means fringes coincide
$n_{1} λ_{1} = n_{2} λ_{2}$
$(n + 4) 5200 Å = (n) 7800 Å$
$(n + 4) 4 = 6 n$
$n = 8$

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