A double slit setup is shown in the figure. One of the slits is in medium 2 of refractive index ...

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A double slit setup is shown in the figure. One of the slits is in medium 2 of refractive index \( n_{2} \). The other slit is at the interface of this medium with another medium 1 of refractive index \( n_{1}\left(\neq n_{2}\right) \). The line joining the slits is perpendicular to the interface and the distance between the slits is \( d \). The slit widths arc much smaller than \( d \). A monochromatic parallel beam of light is incident on the slits from medium 1. A detector is placed in medium 2 at a large distance from the slits, and at an angle \( \theta \) from the line joining them, so that \( \theta \) equals the angle of refraction of the beam. Consider two approximately parallel rays from the slits received by the detector.
(a) The phase difference between the two rays is independent of \( d \).
(b) The two rays interfere constructively at the detector.
(c) The phase difference between the two rays depends on \( n \). but is independent to \( n y \).
(d) The phase difference between the two rays vanishes only for certain values of \( d \) and the angle of incidence of the beam, with \( \theta \) being the corresponding angle of refraction.
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