A double slit arrangement is illuminated first with red, then with blue light.
a. which one has wider fringes?
b. which one produces more fringes?
red
To determine which light color (red or blue) has wider fringes and which one produces more fringes in a double-slit arrangement, we can consider the equation for fringe width and the relationship between fringe width and wavelength.
a. To find out which light color has wider fringes, we need to know the relationship between fringe width and wavelength. The fringe width (W) is given by the equation:
W = λ * L / d
where λ is the wavelength of light, L is the distance between the screen and the double-slit arrangement, and d is the distance between the slits.
As we can see from the equation, the fringe width is directly proportional to the wavelength of light. Therefore, the longer wavelength light (red light) will have wider fringes compared to the shorter wavelength light (blue light).
Therefore, the red light will have wider fringes in the double-slit arrangement.
b. To determine which light color produces more fringes, we need to take into account the interference pattern created. The number of fringes formed depends on the number of bright or dark spots (interference maxima or minima) observed on the screen.
The equation for the number of fringes (m) is given by:
m = L * Δφ / λ
where Δφ is the phase difference between the two interfering waves.
The phase difference depends on the path difference, which is given by:
Δx = d * sin(θ)
where d is the distance between the slits and θ is the angle between the line connecting the two slits and the line connecting the slits to the screen.
We can observe that the path difference also depends on the wavelength (λ) of light. The path difference increases with the decrease in the wavelength of light.
Hence, since blue light has a shorter wavelength compared to red light, it will have more fringes in the double-slit arrangement.
Therefore, the blue light will produce more fringes.