Final answer:
The distance between fringes in Young's double-slit experiment is given by Δy = xλ/d, where x is the distance between the double slits and the screen, λ is the wavelength of the incident light, and d is the distance between the double slits. Therefore, when the intensity at a distance β/4 is given by I0/4, it means that the fringe width is quadrupled and the original intensity I0 is divided by 4.
Step-by-step explanation:
According to the equation for the fringe width in Young's double-slit experiment, the distance between fringes, denoted by Δy, is given by Δy = xλ/d, where x is the distance between the double slits and the screen, λ is the wavelength of the incident light, and d is the distance between the double slits.
Therefore, the distance between fringes is directly proportional to the wavelength of the incident light. So, if the intensity at a distance β/4 is given by I0/4, it means that the fringe width is quadrupled (since each fringe represents a change in path difference of λ/2) and the original intensity I0 is divided by 4. Therefore, the correct answer is (a) I0/4.