In a Young's double slit experiment using monochromatic light, the fringe pattern shifts by a certain distance on the screen when a mica sheet of refractive index 1.6 and thickness 1.964 microns is introduced in the path of one of the interfering waves. The mica sheet is then removed and the distance between the slits and screen is doubled. It is found that the distance between successive maxima now is the same as observed fringe shift upon the introduced of the mica sheet . Calculate the wavelength of the monochromatic light used in the experiment .

Explanation

To solve the problem step by step, we will analyze the situation described in the Young's double slit experiment and apply the relevant formulas.

### Step 1: Understand the Problem
In the experiment, a mica sheet with a refractive index of 1.6 and a thickness of 1.964 microns is introduced in the path of one of the interfering waves, causing a fringe shift. After removing the mica sheet, the distance between the slits and the screen is doubled, and the distance between successive maxima is found to be equal to the fringe shift caused by the mica sheet.

### Step 2: Write the Formula for Fringe Width
The fringe width (β) in a Young's double slit experiment is given by the formula:
\[
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