Question

While conducting the Young's double slit experiment, a student replaced the two slits with a large opaque plate in the x-y plane containing two small holes that act as two coherent point sources $(S_1,S_2)$ emitting light of wavelength 600 $nm$. The student mistakenly placed the screen parallel to the $x-z$ plane (for $z>0$) at a distance $D=3m$, from the mid-point of $S_1,S_2$, as shown schematically in the figure. The distance between the sources $d=0.6003mm$. The origin O is at the intersection of the screen and the line joining $S_1,S_2$. Which of the following is(are) true of the intensity pattern on the screen?

• A. Semi circular bright and dark bands centered at point O
• B. The region very close to the point O will be dark
• C. Straight bright and dark bands parallel to the x-axis
• D. Hyperbolic bright and dark bands with foci symmetrically placed about O in the x-direction.

Answer 1

Answer: (A), (B)

The correct options are
A Semi circular bright and dark bands centered at point O
B The region very close to the point O will be dark


Fringes will be semi circular from YDSE theory.

The screen viewed from the front would look like
Here, at every point in the semi circle will have same path diffrence $\Delta x$
hence semicurcular bright and dark fringes will appear.
$\therefore$ option C and D are wrong

Now to find the path diffrence at O $\Delta x_o=d$
let us assume that $n\lambda =d$ $n=\frac{d}{\lambda }=\frac{0.6003mm}{600\times {10}^{-9}m}=1000.5$

Hence at O, $\Delta x=1000\lambda +\frac{\lambda }{2}$

Hence it will be dark at O.
Which corresponds to minima. So we can say centre point O is minima and will be dark.

$\therefore$ answer is A and B.