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QJEEM23Ph80a9: JEE Main 2023 Physics - Class 12 JEEM23Ph80a9 Solution: As shown in the figure, in Young's double slit experiment, a…

As shown in the figure, in Young's double slit experiment, a thin plate of thickness t=10μm 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 xβ0.β0 is the fringe-width befor the insertion of the plate. The value of the x is _____________.

JEE Main 2023 (Online) 1st February Evening Shift Physics - Wave Optics Question 50 English

Step-by-Step Verified Solution

Given t=10×10−6 m\mathrm{t}=10 \times 10^{-6} \mathrm{~m}

μ=1.2λ=500×10−9 m

When the glass slab inserted infront of one slit then the shift of central fringe is obtained by

t=nλ(μ−1)\mathrm{t}=\frac{\mathrm{n} \lambda}{(\mu-1)}

⇒10×10−6=n×500×10−9(1.2−1)\Rightarrow \quad 10 \times 10^{-6}=\frac{\mathrm{n} \times 500 \times 10^{-9}}{(1.2-1)}

⇒ 10×10−6=n×500×10−90.210 \times 10^{-6}=\frac{\mathrm{n} \times 500 \times 10^{-9}}{0.2}

⇒ n=4\mathrm{n}=4

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