Explanation
Location of bright Fringes is given by Xn = nλD/a
Where n = nth bright fringe
λ=wave length
D = distance between slit and screen
a is slit width
Fringe width is equal to separation between two consecutive bright or dark fringes
β= λD/a
Angular fringe width is angle subtended by fringe width at slits
Ө= β/D
Therefore Ө=λ/a
Fringe width is given by,
β=λDd
Where, λ is the wavelength of light, D is the distance from slit to screen and d is the slit width.
We know,
c=λv
c is speed of light and ν is frequency of light.
If ν is doubled, then,
c=λ′2v=λv
⟹λ′=λ2
So, the fringe width becomes,
β′=λ′Dd=12λDd=β2
Thus, the fringe width becomes half of the original value when the frequency of light is doubled.
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