In Young's double-slit experiment, the fringe width is defined as the separation between successive bright or dark fringes and is calculated using the formula:
\[
\beta = \frac{\lambda D}{d}
\]
where:
- \( \beta \) represents the fringe width,
- \( \lambda \) is the wavelength of the incident light,
- \( D \) denotes the distance from the slits to the screen, and
- \( d \) is the separation between the two slits.
Explanation:
- The fringe width (\( \beta \)) is directly proportional to the light's wavelength (\( \lambda \)). Consequently, any alteration in wavelength will result in a proportional change in fringe width.
- Substituting green light (shorter wavelength) with red light (longer wavelength) increases the wavelength (\( \lambda \)). This increase in wavelength directly leads to an increased fringe width.
Conclusion:
Given that red light possesses a greater wavelength than green light, replacing green light with red light will result in an enlarged fringe width of the interference pattern, provided that the light intensity and other experimental parameters are held constant.