MCQ
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 $\left(S_1, S_2\right)$ emitting light of wavelength $600 \mathrm{~nm}$. The student mistakenly placed the screen parallel to the $x-z$ plane (for $z>0$ ) at a distance $D=3 \mathrm{~m}$ from the mid-point of $S_1 S_2$, as shown schematically in the figure. The distance between the sources $d=0.6003 \mathrm{~mm}$. The origin $\mathrm{O}$ 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?

($A$) Straight bright and dark bands parallel to the $x$-axis

($B$) The region very close to the point $O$ will be dark

($C$) Hyperbolic bright and dark bands with foci symmetrically placed about $\mathrm{O}$ in the $x$-direction

($D$) Semi circular bright and dark bands centered at point $\mathrm{O}$

  • $B,C$
  • B
    $B,D$
  • C
    $B,A$
  • D
    $A,C$

Answer

Correct option: A.
$B,C$
a
$(B)$ Seml clrcular bright and dark bands centred at polnt $O$

$(C)$ The reglon very close to the polnt $O$ will be dark

Since $S _1 S_2$ line is perpendicular to screen shape of pattern is concentric semicircle

$\text { At } O , \frac{2 \pi}{\lambda}\left( S _1 O - S _2 O \right)$

$=\frac{2 \pi \times 0.6003 \times 10^{-3}}{600 \times 10^{-9}}=2001 \pi$

$\therefore$ darkness close to $O$ .

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