In a Young double slit experiment, the wavelength of incident light is 6000 , the separation between slits

Question

In a Young double slit experiment, the wavelength of incident light is 6000 $Å$ , the separation between slits $S_{1}$ and $S_{2}$ is 5 cm and the distance between slits plane and screen is 50 cm, as shown in the figure below. If the resultant intensity at P is equal to the intensity due to individual slits, the path difference between interfering waves is ______ $Å$ . [2026]

Smart Achievers · Accepted Answer

(3)

$I_{p} = I_{0} = 4 I_{0} \cos^{2} \frac{Δ ϕ}{2}$

$\cos \frac{Δ ϕ}{2} = \frac{1}{2} \Rightarrow Δ ϕ = \frac{2 π}{3}$

$\frac{2 π}{λ} Δ x = Δ ϕ = \frac{2 π}{3}$

$Δ x = \frac{λ}{3} = 2000 Å$

Solution

1 4000

2 3000

3 2000

4 1000

Ans.
(3)

$I_{p} = I_{0} = 4 I_{0} \cos^{2} \frac{Δ ϕ}{2}$

$\cos \frac{Δ ϕ}{2} = \frac{1}{2} \Rightarrow Δ ϕ = \frac{2 π}{3}$

$\frac{2 π}{λ} Δ x = Δ ϕ = \frac{2 π}{3}$

$Δ x = \frac{λ}{3} = 2000 Å$

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