Final answer:
In Young's double-slit experiment, the separation between adjacent fringes is given by Δy = xλ/d. By rearranging the formula and plugging in the values, we can calculate the distance between the slits and the separation between fringes for a different wavelength of light.
Step-by-step explanation:
According to Young's double-slit experiment, the separation between adjacent fringes, Δy, is given by the formula Δy = xλ/d, where x is the distance between the slits and the screen, λ is the wavelength of light, and d is the distance between the slits. In this case, we are given that for a wavelength of 425 nm, the separation between the second-order bright fringe and the central bright fringe is 0.0200 m.
Using the given values, we can calculate the value of d by rearranging the formula as d = xλ/Δy. Plugging in the values, we have d = (0.0200 m * (425 nm * 10^-9 m/nm)) / (2 * 2), which simplifies to d = 0.0085 m.
To find the separation, y, when the light has a wavelength of 553 nm, we can rearrange the formula as y = xλ/d.
Plugging in the values, we have y = (0.0085 m * (553 nm * 10^-9 m/nm)) / 2 = 2.44 x 10^-6 m or 2.44 μm.