As shown in the figure, in Young's double slit experiment, a thin plate of thickness and refractive index is inserted infront of slit . The experiment is conducted in air () and uses a monochromatic light of wavelength . [2023]

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Solution

Q.
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 $S_{1}$ . 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 $x β_{0}$ . $β_{0}$ is the fringe-width before the insertion of the plate. The value of the $x$ is ________ . [2023]

Ans.
(4)

$Fringe shift S = \frac{t (μ - 1)}{λ} β_{0}$

$= \frac{10 \times 10^{- 6} (1.2 - 1)}{5 \times 10^{- 7}} β_{0} = x β_{0}$

$\Rightarrow x = \frac{10^{- 5} \times 0.2}{5 \times 10^{- 7}} = 4$

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