Kerala KEAM 5 June 2024 Solved Paper

In a Young's double slit experiment, the fringe width $\beta$ is given by the formula:$$\beta = \frac{\lambda D}{d}$$where:- $\lambda$ is the wavelength of the light,- $D$ is the distance between the slits and the screen,- $d$ is the distance between the slits.In this case, we are told that the distance of the screen ($D$) and the slit separation ($d$) remain constant. Therefore, the fringe width $\beta$ is directly proportional to the wavelength $\lambda$.Thus, the fringe width ratio for wavelengths in the ratio 2:3:4 will also be in the same ratio:$$\frac{\beta_1}{\beta_2} = \frac{\lambda_1}{\lambda_2} = \frac{2}{3} \quad and \quad \frac{\beta_2}{\beta_3} = \frac{\lambda_2}{\lambda_3} = \frac{3}{4}$$So, the corresponding fringe width ratio will be 2:3:4.Therefore, the correct answer is:$$\boxed{C) 2:3:4}$$ Quick Tip: In a Young's double slit experiment, the fringe width is directly proportional to the wavelength. If the wavelength changes, the fringe width will change in the same ratio.