In a Young's double slit experiment, if there is no initial phase difference between the light from the two slits, a point on the screen corresponding to the fifth minimum has path difference. [2019]

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Solution

Q.
In a Young's double slit experiment, if there is no initial phase difference between the light from the two slits, a point on the screen corresponding to the fifth minimum has path difference. [2019]

1 $5 \frac{λ}{2}$

2 $10 \frac{λ}{2}$

3 $9 \frac{λ}{2}$

4 $11 \frac{λ}{2}$

Ans.
(3)

Given, there is no initial phase difference.

$∴$ Initial phase = $δ$ = 0

Again, Phase difference $= \frac{2 π}{λ} \times$ Path difference

$\Rightarrow δ' = \frac{2 π}{λ} \times Δ x \Rightarrow Δ x = \frac{λ}{2 π} \times δ'$

Now, for the fifth minima we will consider $n = 4$ as initial phase difference is zero.

$∴$ For fifth minimum, $δ' = (8 + 1) π = 9 π$

$∴$ Path difference, $Δ x = \frac{λ}{2 π} \times 9 π = \frac{9 λ}{2}$

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