In YDSE, D=1m, d=4mm and $λ = \frac{1}{2} mm$ in the figure shown, a parallel beam of light is incident on the plane of the slits of YDSE. Light incident on the slit $S_{1}$ passes through a medium of variable refractive index $μ = (2 x + 1)$ (where x is the distance from the plane of slits in mm) up to a distance $l = 1 mm$ before falling on $S_{1}$ rest of the space filled with air. Then choose the correct option(s):

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Position of central bright fringe is at a distance $y = \frac{1}{\sqrt{3}}$ m above the central line

Position of central bright fringe is at a distance $y = \frac{1}{2} m$ above the central line

Number of maxima obtained on the screen is 8

Number of maxima obtained on the screen is 7

answer is A, D.

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Detailed Solution

For central height fringe $d \sin θ = 2 m m$

$4 m m \sin θ = 2 m m θ = 30^{0} \tan 30^{0} = \frac{y}{2} y = \frac{1}{\sqrt{3}} m .$

For bright fringe $(d \sin θ \pm 2) = n λ$ where n is 0, 1, 2, 3…

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