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  4. In Young's double-slit experiment, the y-coordinates of central maxima and 10 th maxima are 2 cm and 5 cm, respectively. When the YDSE apparatus is immersed in a liquid of refractive index 1.5, the corresponding y-coordinates will be

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Q. In Young's double-slit experiment, the $y$-coordinates of central maxima and $10$ th maxima are $2 \,cm$ and $5 \,cm$, respectively. When the YDSE apparatus is immersed in a liquid of refractive index $1.5$, the corresponding $y$-coordinates will be

Wave Optics

Solution:

Fringe width, $\beta \propto \lambda$. Therefore, $\lambda$ and hence $\beta$ will decrease $1.5$ times when immersed in the liquid. The distance between central maxima and 10th maxima is $3\, cm$ in vacuum. When immersed in the liquid, it will reduce to $2 \,cm$. Position of central maxima will not change while $10$ th maxima will be obtained at $y=4 \,cm$.