As shown in the figure, in Young’s double slit experiment, a thin plate of thickness \( t = 10 \, \mu \text{m} \) and refractive index \( \mu = 1.2 \) is inserted infront of slit \( S_{1} \). The experiment is conducted in air \( (\mu = 1) \) and uses a monochromatic light of wavelength \( \lambda = 500 \, \text{nm} \). Due to the insertion of the plate, central maxima is shifted by a distance of \( x \beta_{0} \), \( \beta_{0} \) is the fringe-width before the insertion of plate. The value of the \( x \) is _______.
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