Question

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 $\alpha \times 10^{-\beta }cm/s$ upward in scientific notation. The value of $\alpha +\beta$ is ________.

Answer 1

Answer: 5

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

$y=\frac{Dd}{2x}\Rightarrow \frac{dy}{dt}=-\frac{Dd}{2x^2}\left(\frac{dx}{dt}\right)$
$=\left(\frac{1\times 0.01}{2\times 0.5\times 0.5}\right)\times (0.001)=0.02mm/s$
$\Rightarrow y=2\times 10^{-3}cm/s$
$\Rightarrow \alpha +\beta =5$