Question

Monochromatic light of green color is used in Young’s double slit experiment and an interference pattern is observed on a screen. If the green light is replaced by red monochromatic light of the same intensity, how will the fringe width of the interference pattern be affected? Justify your answer.

Hint:

The fringe width in Young’s double-slit experiment is proportional to the wavelength of the light used. Replacing green light with red light (which has a longer wavelength) will increase the fringe width.

Answer 1

In Young’s double slit experiment, the fringe width (the distance between two consecutive bright or dark fringes) is given by the formula: \[ \beta = \frac{\lambda D}{d} \] where:
- \( \beta \) is the fringe width,
- \( \lambda \) is the wavelength of the light used,
- \( D \) is the distance between the slits and the screen,
- \( d \) is the distance between the two slits. Explanation: - The fringe width is directly proportional to the wavelength \( \lambda \) of the light used. Therefore, if the wavelength of the light is changed, the fringe width will also change in proportion to the wavelength. - When green light (which has a relatively shorter wavelength) is replaced by red light (which has a longer wavelength), the wavelength \( \lambda \) of the light increases. As a result, the fringe width will also increase. Conclusion: Since the wavelength of red light is larger than that of green light, the fringe width of the interference pattern will increase when the green light is replaced by red light, assuming the intensity and other experimental conditions remain the same.