In young's double slit experiment path differences at two points A and B between two waves emerging from slits s1 and s2 are λ6 and λ4 respectively. Then the ratio of intensities at A and B will be :

ϕA=2πλ.λ6=π3 and ϕB=2πλ.λ4=π2 ∴IA=I+I+2II.cos ϕA=2I+2I cos60o=3I IB=I+I+2II.cos ϕB=2I+2I cos90o=2I ∴IA : IB=3 : 2

In young's double slit experiment path differences at two points A and B between two waves emerging from slits s1 and s2 are λ6 and λ4 respectively. Then the ratio of intensities at A and B will be :

ϕA=2πλ.λ6=π3 and ϕB=2πλ.λ4=π2 ∴IA=I+I+2II.cos ϕA=2I+2I cos60o=3I IB=I+I+2II.cos ϕB=2I+2I cos90o=2I ∴IA : IB=3 : 2

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In young's double slit experiment path differences at two points A and B between two waves emerging from slits s₁ and s₂ are $\frac{λ}{6} and \frac{λ}{4}$ respectively. Then the ratio of intensities at A and B will be :

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3 : 1

2 : 1

3 : 2

4 : 3

answer is A.

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Detailed Solution

$ϕ_{A} = \frac{2 π}{λ} . \frac{λ}{6} = \frac{π}{3} and ϕ_{B} = \frac{2 π}{λ} . \frac{λ}{4} = \frac{π}{2} ∴ I_{A} = I + I + 2 \sqrt{I} \sqrt{I} . \cos ϕ_{A} = 2 I + 2 I \cos 60^{o} = 3 I I_{B} = I + I + 2 \sqrt{I} \sqrt{I} . \cos ϕ_{B} = 2 I + 2 I \cos 90^{o} = 2 I ∴ I_{A} : I_{B} = 3 : 2$