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Question:
how fringe width change if apparatus of YDSE is dipped in water
Answer:

First, note that the wavelength of light will decrease in water. From c=fλc=fλ, and remembering that frequency doesn t depend on the medium, wavelength is proportional to speed of light in the medium. Using the formula for angular separation of the bright fringes: 

asinθ=mλ,m=0,1,2,⋯asin⁡θ=mλ,m=0,1,2,⋯

you can see that the separation decreases with wavelength. 

We can think of it intuitively in the following manner. In air, the first minimum occurs when the path length between slits differs by λ/2λ/2. In water, the wavelength decreases, so the initial path difference now contains more than half a wavelength: the angle is too large to be the first minimum! You ve got to decrease the angle to recover the difference of half a wavelength.

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