Final answer:
The separation between the first and third maxima in a multiple-slit interference pattern caused by monochromatic light can be calculated using the wavelength of the light, the slit spacing, and the distance to the screen. The correct separation is 5.5 mm.
Step-by-step explanation:
The question involves calculating the separation between the first and third maxima in a multiple-slit interference pattern created by monochromatic light. To solve this problem, we first need to find the wavelength of the light since we're given its frequency. The equation c = λf can be used, where λ is the wavelength, f is the frequency, and c is the speed of light (3 x 10⁸ m/s).
Once the wavelength is determined, we can use the multiple-slit interference equation λ = dsinθ, where d is the distance between the slits, θ is the angle of the maxima, and n is the order number of the maxima. We find the angles for the first and third maxima using n=1 and n=3, respectively. By using the small angle approximation sinθ ≈ tanθ = y/L (where y is the separation on the screen and L is the distance from the slits to the screen), we can solve for the separation between the maxima.
The calculations yield the separation between the first and third maxima. Among the provided options, option (a) 5.5 mm is the correct answer for the separation between the first and third maxima on the screen.