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  4. The figure shows a Young's double-slit experiment where, P and Q are the slits. The path lengths P X and Q X are n λ and (n+2) λ respectively, where n is a whole number and λ is the wavelength. Taking, path difference at the central fringe as zero, what is formed at X ?

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Q. The figure shows a Young's double-slit experiment where, $P$ and $Q$ are the slits. The path lengths $P X$ and $Q X$ are $n \lambda$ and $(n+2) \lambda$ respectively, where $n$ is a whole number and $\lambda$ is the wavelength. Taking, path difference at the central fringe as zero, what is formed at $X$ ?Physics Question Image

Wave Optics

Solution:

Path difference $=Q X-P X=(n+2) \lambda-n \lambda=2 \lambda$ ... (i)
For constructive interference or bright band,
Path difference $=\Delta x=n \lambda$ (where, $n=1,2, \ldots$ )
From Eq. (i), it is obvious that second bright band is formed as $n=2$.