In Young's double slit experiment, an interference pattern is obtained on a screen by a light of wavelength 6000 mathringA coming from the coherent sources S1 and S2. At certain point P on the screen third dark fringe is formed. Then the path difference S1 P-S2 P in microns is

Question

In Young's double slit experiment, an interference pattern is obtained on a screen by a light of wavelength 6000 mathringA coming from the coherent sources S1 and S2. At certain point P on the screen third dark fringe is formed. Then the path difference S1 P-S2 P in microns is (A) 0.75 (B) 1.5 (C) 3.0 (D) 4.5

Tardigrade Admin · Accepted Answer

For dark fringe at P S1 P-S2 P=Δ=(2 n-1) λ / 2 Here n=3 and λ=6000 mathringA So, Δ=(5 λ/2)=5 × (6000/2) =15000 mathringA=1.5 micron

Q. In Young's double slit experiment, an interference pattern is obtained on a screen by a light of wavelength 6000A˚ coming from the coherent sources S1​ and S2​. At certain point P on the screen third dark fringe is formed. Then the path difference S1​P−S2​P in microns is

0.75

1.5

3.0

4.5

For dark fringe at P S1​P−S2​P=Δ=(2n−1)λ/2 Here n=3 and λ=6000A˚ So, Δ=25λ​=5×26000​ =15000A˚=1.5 micron

For dark fringe at $P$
$S_{1} P - S_{2} P = Δ = (2 n - 1) λ /2$
Here $n = 3$ and $λ = 6000 \overset{˚}{A}$
So, $Δ = \frac{5 λ}{2} = 5 \times \frac{6000}{2}$
$= 15000 \overset{˚}{A} = 1.5$ micron