Question

In Young's Double Slit Experiment, monochromatic light of wavelength \( \lambda \) is used. The slits are separated by a distance \( d \), and the screen is placed at a distance \( D \) from the slits. If the fringe width is observed to be \( \beta \), and the distance between the slits and the screen is doubled, what will be the new fringe width?

• A. \( \beta \)
• B. \( 2\beta \)
• C. \( \frac{\beta}{2} \)
• D. \( 4\beta \)

Hint:

Remember, in Young's Double Slit Experiment, the fringe width is directly proportional to the distance between the slits and the screen. Doubling this distance will double the fringe width.

Answer 1

The Correct Option is B

In 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. If the distance between the slits and the screen is doubled, then the new distance becomes \( 2D \). Substituting this into the fringe width formula: \[ \beta_{\text{new}} = \frac{\lambda (2D)}{d} = 2 \times \frac{\lambda D}{d} = 2\beta \] Thus, the new fringe width will be \( 2\beta \).