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 (S1$$,$$S2) emitting light of wavelength $$600nm$$. 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 $$S1S2$$, 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 $$S1S2$$, which of the following $$is(are)$$ true of the intensity pattern on the screen?

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 (S1$$,$$S2) emitting light of wavelength $$600nm$$. 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 $$S1S2$$, 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  $$S1S2$$, which of the  following $$is(are)$$ true of the intensity pattern on the screen?

Infinity Learn · Accepted Answer

Locus of points ‘P’ such that  $$S1P$$−$$S2P$$ is constant is a circle. As per given screen, only semicircle is formed. Hence options (B) (D) are $$wrong(C)$$ path difference at ‘O’ is $$x=d$$ $$=$$ $$6.003$$×$$10$$−$$4mx$$λ$$=6.003$$×$$10$$−$$46$$×$$10$$−$$7=1000.5$$ xλ$$=1000$$λ$$+$$λ$$2$$⇒  dark fringe is formed at ‘O’

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