In a double slit experiment the distance between the slits is 0.1 cm and the screen is placed at 50 cm from the slits plane. When one slit is covered with a transparent sheet having thickness t and refractive index n(= 1.5), the central fringe shifts by 0.2 cm. The value of t is ____ cm.

### Related Formula textShift (x) = fracDd (mu - 1)t$$\text{Shift } (x) = \frac{D}{d} (\mu - 1)t$$ Alternatively written: d left(fracxDright) = (mu - 1)t$d \left(\frac{x}{D}\right) = (\mu - 1)t$ ### Core Logic Given parameters: Distance between slits, d = 0.1text cm$d = 0.1\text{ cm}$ Distance to screen, D = 50text cm$D = 50\text{ cm}$ Fringe shift, x = 0.2text cm$x = 0.2\text{ cm}$ Refractive index, mu = 1.5$\mu = 1.5$ ### Step 1: Calculate Thickness Rearranging the formula for thickness t$t$: t = fracx cdot dD(mu - 1)$$t = \frac{x \cdot d}{D(\mu - 1)}$$ t = frac(0.2)(0.1)50(1.5 - 1)$$t = \frac{(0.2)(0.1)}{50(1.5 - 1)}$$ t = frac0.0250(0.5) = frac0.0225$$t = \frac{0.02}{50(0.5)} = \frac{0.02}{25}$$ t = 8 times 10^-4text cm$$t = 8 \times 10^{-4}\text{ cm}$$ ### Pattern Recognition Direct plug-and-play into the slab shift formula. Working completely in cm avoids unit conversion errors as long as all given lengths (x$x$, d$d$, D$D$) are consistently in cm and the answer is requested in cm. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Wave Optics