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,
$$\beta=\dfrac{\lambda D}{d}$$
Where, $$\lambda$$ is the wavelength of light, $$D$$ is the distance from slit to screen and $$d$$ is the slit width.
We know,
$$c=\lambda v$$
$$c$$ is speed of light and $$ν$$ is frequency of light.
If $$ν$$ is doubled, then,
$$c=\lambda' 2v=\lambda v$$
$$\implies \lambda'=\dfrac{\lambda}{2}$$
So, the fringe width becomes,
$$\beta'=\dfrac{\lambda' D}{d}=\dfrac 12 \dfrac{\lambda D}{d}=\dfrac{\beta}{2}$$
Thus, the fringe width becomes half of the original value when the frequency of light is doubled.
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