Question

In an Young double slit experiment without varying the distance of the screen and the slit separation, if the wavelength of monochromatic source is changed one by one in the ratio 2:3:4, then the corresponding fringe widths measured will be in the ratio:

• A. 4:3:2
• B. 1:2:3
• C. 2:3:4
• D. 6:4:3
• E. 3:4:6

Hint:

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.

Answer 1

The Correct Option is C

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: \[ \boxed{{C) 2:3:4}} \]