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Q.

In Young’s double-slit experiment using monochromatic light of wave length $λ$ , the intensity of light a point on the screen where path difference is $λ$ , is K units. The intensity of light at a point where path difference is $λ$ /3

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a

K/4

b

K/3

c

K/2

d

K

answer is A.

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Detailed Solution

For waves of intensity I₀ each, the resulting interference intensity is given as $I_{R} = 4 I_{0} \cos^{2} \frac{δ}{2}$
were phase difference $δ = \frac{2 π}{λ} \times Δ$
Initially $Δ = λ \Rightarrow δ = \frac{2 π}{λ} \times λ = 2 π$
$\begin{array}{l} \Rightarrow I_{g} = K = 4 I_{0} \cos^{2} π = 4 I_{0} \\ Later Δ = \frac{λ}{3} \Rightarrow δ = \frac{2 π}{λ} \times \frac{λ}{3} = \frac{2 π}{3} \\ \Rightarrow I_{R} = 4 I_{0} \cos^{2} (\frac{π}{3}) = 4 I_{0} (\frac{1}{4}) = I_{0} = \frac{K}{4} \end{array}$

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