Question

In a double-slit arrangement , the slits are separated by a distance equal to $100$ times the wavelength of the light passing through the slits.
(a) What is the angular separations in radians between the central maximum and an adjacent maximum ?
(b) What is the distance between these maxima on a screen $50.0cm$ from the slits ?

Answer 1

(a) The conditions for maximum in Young's experiment is given by:
$d\sin \left(\theta \right)=m\lambda$ $m=0,1,2$ ..
The angle between the central maximum and it's adjacent can be determined by setting $m$ equals to $1$, so;
$d\sin \left(\theta \right)=\lambda$
$\theta ={\sin }^{-1}\left(\frac{\lambda }{d}\right)$
but $d=100\lambda$
$\theta ={\sin }^{-1}\left(\frac{\lambda }{100\lambda }\right)$
$\theta ={\sin }^{-1}\left(\frac{1}{100}\right)$
$={0.573}^{\circ }=0.01rad$
$\theta =0.01rad$
(b) The distance between the central axis and the first maximum is given by:
$y=L\sin \left(\theta \right)$
where $L$ is the distance between the slits and the screen, so;
$y=\left(50.0cm\right)\sin \left({0.573}^{\circ }\right)$
$y=0.50cm$