In a typical Young’s double slit experiment a point source of monochromatic light is kept as shown in the figure. If the source is given an instantaneous velocity v=1mm per second towards the screen, then the instantaneous velocity of central maxima is given as $α \times 10^{- β} c m / s$ upward in scientific notation. Find the value of $\frac{β}{α}$ .

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Detailed Solution

The central maxima $\frac{d y}{D} = \sqrt{d^{2} + x^{2}} - x = [1 + \frac{d^{2}}{{2 x}^{2}}] - x = \frac{d^{2}}{2 x}$

$y = \frac{D d}{2 x} \Rightarrow \frac{d y}{d t} = - \frac{D d}{2 x^{2}} (\frac{d x}{d t}) = (\frac{1 \times 0.01}{2 \times 0.5 \times 0.5}) \times (0.001) 0.02 m m / s \Rightarrow y = 2 \times 10^{2} c m / s \Rightarrow α + β = 4$

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