In Young's double-slit arrangement,the screen | vedclass

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(B) Let $d$ be the distance between the slits and $\lambda$ be the wavelength of light used.At $t=0$,the distance between the slits and the screen is

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$\frac{x}{v}$

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(B) Let $d$ be the distance between the slits and $\lambda$ be the wavelength of light used.At $t=0$,the distance between the slits and the screen is $D = x$. The position of the $1^{	ext{st}}$ order maxima at point $A$ is given by $y = \frac{\lambda D}{d} = \frac{\lambda x}{d}$.At time $t$,the distance between the slits and the screen becomes $D_t = x + vt$.The position of the $1^{	ext{st}}$ order minima at point $A$ is given by $y = \frac{\lambda D_t}{2d} = \frac{\lambda (x + vt)}{2d}$.Since the point $A$ remains at the same position $y$,we equate the two expressions:$\frac{\lambda x}{d} = \frac{\lambda (x + vt)}{2d}$$2x = x + vt$$x = vt$$t = \frac{x}{v}$

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