In a Young's double slit experiment, the slit separation $d$ is 0.3 mm and the screen distance $D$ is 1 m. A parallel beam of light of wavelength 600 nm is incident on the slits at angle $α$ as shown in figure. On the screen, the point O is equidistant from the slits and distance PO is 11.0 mm. Which of the following statement(s) is/are correct [2019]

Question

Smart Achievers · Accepted Answer

(3)

Path difference, $D$ $[when α and θ are small]$

(1) For $α = 0$ , path difference

$Δ x = \frac{y d}{D} = \frac{0.3 \times 11}{1000} = 33 \times 10^{- 4} mm$

Now, $\frac{Δ x}{λ} = \frac{33 \times 10^{- 4}}{600 \times 10^{- 6}} = \frac{11}{2}$

$∴$ $Δ x = \frac{11}{2} λ = (2 n - 1) \frac{λ}{2}$

Hence, interference at $P$ is destructive.

(2) Fringe width, $β = \frac{λ D}{d}$ is independent of $α$

(3) For $α = \frac{0.36}{π}$ degree (at point P),

$Δ x = d [α + \frac{y}{D}]$ $= 0.3 \times 10^{- 3} [\frac{0.36}{180} + \frac{11 \times 10^{- 3}}{1}] m = 3900 nm$

Now, $\frac{Δ x}{λ} = \frac{3900}{600} = \frac{13}{2} λ$

Hence, destructive interference at $P$

(4) For $α = \frac{0.36}{π}$ degree (at point O)

$Δ x = d α = 0.3 \times 10^{- 3} \times \frac{0.36}{180} = 600 \times 10^{- 9} m = 600 nm$

Now, $\frac{Δ x}{λ} = 1$ $\Rightarrow Δ x = 1 λ$

Hence, constructive interference at $O$

Solution

1 For $α = 0$ , there will be constructive interference at point $P$

2 Fringe spacing depends on $α$

3 For $α = \frac{0.36}{π}$ degree, there will be destructive interference at point $P$

4 For $α = \frac{0.36}{π}$ degree, there will be destructive interference at point $O$

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Solution

1 For α=0, there will be constructive interference at point P

2 Fringe spacing depends on α

3 For α=0.36π degree, there will be destructive interference at point P

4 For α=0.36π degree, there will be destructive interference at point O

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1 For $α = 0$ , there will be constructive interference at point $P$

2 Fringe spacing depends on $α$

3 For $α = \frac{0.36}{π}$ degree, there will be destructive interference at point $P$

4 For $α = \frac{0.36}{π}$ degree, there will be destructive interference at point $O$