BITSAT 2024 Shift 1 Paper

In the Young's Double Slit Experiment (YDSE), for monochromatic light shining on a screen 1.80 m away from two slits separated by 2.08 mm , the separation of the first and second order bright fringes is 0.553 mm . To find the wavelength of light used, we use the following calculations:The position of the first bright fringe is given by:$y_1 = \frac{\lambda D}{d}$The position of the second bright fringe is:$y_2 = \frac{2\lambda D}{d}$The separation between the first and second order bright fringes is:$y_2 - y_1 = \frac{2\lambda D}{d} - \frac{\lambda D}{d} = \frac{\lambda D}{d}$From this, we can derive the formula for the wavelength $\lambda$ as:$\lambda = \frac{(y_2 - y_1) d}{D}$Substituting the given values into this equation:$\lambda = \frac{0.553 \times 10^{-3} \times 2.08 \times 10^{-3}}{1.8}$Solving this gives:$\lambda = 639 \times 10^{-9}\ \text{m}$Therefore, the wavelength of the light used is:$\lambda = 639\ \text{nm}$