State two conditions to obtain sustained interference of light. In young's double slit experiment, using light of wavelength 400 nm, interference fringes of width X are obtained. The wavelength of light is increased to 600 nm and the separation between the slits is halved. if one wants the observed fringe width on the screen to be the same in the two cases, find the ratio of the distance between the screen and the plane of the slits in the two arrangements.

Explanation

To solve the problem step by step, we will first state the two conditions for sustained interference of light, and then we will find the ratio of the distances between the screen and the plane of the slits in the two arrangements.

### Step 1: State the conditions for sustained interference of light
1. **Coherent Sources**: The light sources must be coherent, meaning they should emit light waves that have a constant phase difference.
2. **Monochromatic Light**: The light used should be monochromatic (of a single wavelength) to ensure that the interference pattern is stable and clear.

### Step 2: Write down the formula for fringe width
The fringe width (β) in Young’s double slit experiment is given by the formula:
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