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  4. Light of wavelength 500 nm is used to form interference pattern in Young's double slit experiment. A uniform glass plate of refractive index 1.5 and thickness 0.1 mm is introduced in the path of one of the interfering beams. The number of fringes which will shift the cross wire due to this is

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Q. Light of wavelength $500 \,nm$ is used to form interference pattern in Young's double slit experiment. A uniform glass plate of refractive index $1.5$ and thickness $0.1 \,mm$ is introduced in the path of one of the interfering beams. The number of fringes which will shift the cross wire due to this is

Wave Optics

Solution:

The number of fringes shifting is decided by the extra path difference produced by introducing the glass plate. The extra path difference is $(\mu-1) t=n \lambda$ or $(1.5-1) \times 0.1 \times 10^{-3}=n \times 500 \times 10^{-9}$
$=n=100$