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In a typical Young's double silt experiment a point source of monochromatic light is kept as shown in the figure. If the source is given an instantaneous velocity $v = 1 mm$ per second towards the screen as shown, then the magnitude of instantaneous velocity of central maxima is $n \times 10^{- 6} m/s$ . Find the value of n.

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Detailed Solution

For central maxima $(S_{1} S_{2} = d)$
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$\frac{d y}{D} = \sqrt{d^{2} + x^{2}} - x = x [1 + \frac{d^{2}}{2 x^{2}}] - x = \frac{d^{2}}{2 x} y = \frac{D d}{2 x} \frac{d y}{d t} = - \frac{D d}{2 x^{2}} (\frac{d x}{d t}) = - \frac{1 \times 0.01}{2 \times 0.5 \times 0.5} \times (- 0.001)$

$= 0.02 mm$ per second upwards

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In a typical Young's double silt experiment a point source of monochromatic light is kept as shown in the figure. If the source is given an instantaneous velocity v=1 mm per second towards the screen as shown, then the magnitude of instantaneous velocity of central maxima is n×10−6 m/s . Find the value of n.