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  4. As shown in the figure, in Young's double slit experiment, a thin plate of thickness t=10 μ m and refractive index μ=1.2 is inserted infront of slit S1. The experiment is conducted in air (μ-1) and uses a monochromatic light of wavelength λ=500 nm. Due to the insertion of the plate, central maxima is shifted by a distance of x β0 . β0 is the fringe-width befor the insertion of the plate. The value of the x is

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Q. As shown in the figure, in Young's double slit experiment, a thin plate of thickness $t=10\, \mu m$ 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 $\lambda=500\, nm$. Due to the insertion of the plate, central maxima is shifted by a distance of $x \beta_0 . \beta_0$ is the fringe-width befor the insertion of the plate. The value of the $x$ is ___Physics Question Image

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Solution:

Fringe shift $=\frac{t(\mu-1)}{\lambda} B $
$ =\frac{10 \times 10^{-6}(1.2-1)}{5 \times 10^{-7}} B $
$ =\frac{10^{-5} \times 0.2}{5 \times 10^{-7}}=4$