Question

The distance between two slits in a $YDSE$ apparatus is $3mm$ . The distance of the screen from the slits is $1m$ . Microwaves of wavelength $1mm$ are incident on the plane of the slits normally. Find the distance of the first maxima on the screen from the central maxima. Also find the total number of maxima on the screen.

Answer 1

The path difference is YDSE is given as

$\Delta x=d\sin \theta$

$\Delta x=\pm n\lambda$

By using the above two we get

$\sin \theta =\pm \frac{n\lambda }{d}$

By substituting the values given and as we know

$\sin \theta =\pm \frac{n}{3}$

For the 1^st maxima

$\sin \theta =\pm \frac{1}{3}$

The central maxima is

$\tan \theta =\frac{y}{D}$

$\tan \theta =\frac{1}{\sqrt{8}}$

$y=\frac{D}{\sqrt{8}}=35.53cm$

The number of maxima can be possible for the values of $n=0,1,2$

So the total number of maxima present is $5$