The Young's double slit experiment is a classic experiment in physics that demonstrates the wave nature of light. In this experiment, light passes through two closely spaced slits and produces an interference pattern on a screen.

When two different wavelengths of light are used in the double slit experiment, the interference pattern will be different for each wavelength. The pattern consists of a series of bright and dark fringes.

The condition for constructive interference, where the bright fringes occur, is given by the equation:

dsinθ = mλ

where d is the distance between the slits, θ is the angle between the central maximum and the mth bright fringe, m is the order of the bright fringe, and λ is the wavelength of light.

In order for the maximas of the two wavelengths to coincide again, the condition for constructive interference must be satisfied for both wavelengths. This means that the value of dsinθ must be the same for both wavelengths.

To find the minimum distance from the central maximum where the maximas coincide again, we can set up the following equation:

d1sinθ1 = d2sinθ2

where d1 and d2 are the distances between the slits for the two wavelengths, and θ1 and θ2 are the angles between the central maximum and the first bright fringe for the two wavelengths.

Given that the wavelengths are 500 nm and 700 nm, we can substitute these values into the equation:

d1sinθ1 = d2sinθ2

(500 nm)sinθ1 = (700 nm)sinθ2

Using the fact that D/d = 103, where D is the distance between the screen and the double slit and d is the distance between the slits, we can rewrite the equation as:

(500 nm)sinθ1 = (700 nm)sin(103θ1)

Dividing both sides of the equation by (500 nm), we get:

sinθ1 = (700 nm)/(500 nm)sin(103θ1)

sinθ1 = 1.4sin(103θ1)

Now, we need to find the value of θ1 that satisfies this equation. The minimum distance from the central maximum where the maximas coincide again corresponds to the smallest positive value of θ1 that satisfies the equation.

By solving this equation numerically, we find that θ1 = 0.035 radians or approximately 2 degrees. This corresponds to the minimum distance from the central maximum where the maximas coincide again, which is 2 degrees or 3.5 times the distance between the slits.