In a Young's double slit experiment set up, the two slits are kept 0.4 text mm$0.4 \text{ mm}$ apart and screen is placed at 1 text m$1 \text{ m}$ from slits. If a thin transparent sheet of thickness 20 \,mutextm$20 \,\mu\text{m}$ is introduced in front of one of the slits then centre bring fringe shifts by 20 text mm$20 \text{ mm}$ on the screen. The refractive index of transparent sheet is given by fracalpha10$\frac{\alpha}{10}$, where alpha$\alpha$ is ________.

### Related Formula y_textshift = frac(mu - 1)t cdot Dd$$y_{\text{shift}} = \frac{(\mu - 1)t \cdot D}{d}$$ ### Core Logic Introducing a transparent sheet of thickness t$t$ and refractive index mu$\mu$ adds an extra optical path length of (mu - 1)t$(\mu - 1)t$. This translates to a shift of the entire fringe pattern on the screen. Given values: d = 0.4 text mm = 0.4 times 10^-3 text m$d = 0.4 \text{ mm} = 0.4 \times 10^{-3} \text{ m}$ D = 1 text m$D = 1 \text{ m}$ t = 20 \,mutextm = 20 times 10^-6 text m$t = 20 \,\mu\text{m} = 20 \times 10^{-6} \text{ m}$ y_textshift = 20 text mm = 20 times 10^-3 text m$y_{\text{shift}} = 20 \text{ mm} = 20 \times 10^{-3} \text{ m}$ ### Step 1: Substitution and Solving 20 times 10^-3 = frac(mu - 1) times 20 times 10^-6 times 10.4 times 10^-3$$20 \times 10^{-3} = \frac{(\mu - 1) \times 20 \times 10^{-6} \times 1}{0.4 \times 10^{-3}}$$ 20 times 10^-3 = frac(mu - 1) times 20 times 10^-64 times 10^-4$$20 \times 10^{-3} = \frac{(\mu - 1) \times 20 \times 10^{-6}}{4 \times 10^{-4}}$$ 20 times 10^-3 = (mu - 1) times 5 times 10^-2$$20 \times 10^{-3} = (\mu - 1) \times 5 \times 10^{-2}$$ (mu - 1) = frac20 times 10^-35 times 10^-2 = 4 times 10^-1 = 0.4$$(\mu - 1) = \frac{20 \times 10^{-3}}{5 \times 10^{-2}} = 4 \times 10^{-1} = 0.4$$ ### Step 2: Final Conclusion mu = 1 + 0.4 = 1.4$$\mu = 1 + 0.4 = 1.4$$ We are given mu = fracalpha10$\mu = \frac{\alpha}{10}$. fracalpha10 = 1.4 implies alpha = 14$$\frac{\alpha}{10} = 1.4 \implies \alpha = 14$$ ### Pattern Recognition The central fringe always shifts towards the slit covered by the slab. The linear shift y_0 = fracDd(mu-1)t$y_0 = \frac{D}{d}(\mu-1)t$ is independent of the wavelength used. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Wave Optics