Final answer:
The ratio of the slit separation to the slit width in the double-slit interference pattern can be found using the formula: d / a = (Screen distance x Wavelength) / (Number of fringes).
Step-by-step explanation:
The central diffraction peak of the double-slit interference pattern contains nine fringes. The fringes are formed due to the constructive and destructive interference of light waves passing through the two slits.
To find the ratio of the slit separation to the slit width, we need to use the formula:
Number of fringes = (Screen distance x Wavelength) / (Slit separation)
In this case, the number of fringes is 9, and we are looking for the ratio of the slit separation (d) to the slit width (a). Rearranging the formula, we get:
d / a = (Screen distance x Wavelength) / (Number of fringes)
Substituting the given values, we can calculate the ratio.