Optics 6 Question 33
35. 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 $600 mm$. The student mistakenly placed the screen parallel to the $x-z$ plane (for $z>0$ ) at a distance $D=3 m$ from the mid-point of $S _1 S _2$, as shown schematically in the figure. The distance between the source $d=0.6003 mm$. The origin $O$ is at the intersection of the screen and the line joining $S _1 S _2$. (2016 Adv.)
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
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Solution:
Path difference at point $O=d=0.6003 mm$
$$ =600300 nm \text {. } $$
This path difference is equal to $1000 \lambda+\frac{\lambda}{2}$.
$\Rightarrow$ Minima is formed at point $O$.
Line $S _1 S _2$ and screen are $\perp$ to each other so fringe pattern is circular (semi-circular because only half of screen is available)
