The path of the difference between two interfering the waves at a point on the screen -8- The ratio of intensity at this point and that of at the central fringe will be

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YDSE Problems I

The path of t...

Question

The path of the difference between two interfering the waves at a point on the screen $\frac{λ}{8}$ . The ratio of intensity at this point and that of at the central fringe will be

0.853

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8.53

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85.3

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853

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Solution

The correct option is A $0.853$
Let $I_{o}$ be the intensity of single wave
Phase difference $Δ ϕ = 2 π \frac{Δ x}{λ} = 2 π \frac{λ / 8}{λ} = \frac{π}{4}$
Intensity of central fringe $I_{m a x} = I_{o} + I_{o} + 2 \sqrt{I_{o} I_{o}} = 4 I_{o}$
Intensity at required point $I_{p o i n t} = I_{o} + I_{o} + 2 \sqrt{I_{o} I_{o}} cos \frac{π}{4} = (2 + \sqrt{2}) I_{o}$
$\frac{I_{p o i n t}}{I_{m a x}} = \frac{(2 + 1.414)}{4} = 0.853$

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The path of the difference between two interfering the waves at a point on the screen λ8. The ratio of intensity at this point and that of at the central fringe will be

The correct option is A 0.853Let Io be the intensity of single wavePhase difference Δϕ=2πΔxλ=2πλ/8λ=π4Intensity of central fringe Imax=Io+Io+2√IoIo=4IoIntensity at required point Ipoint=Io+Io+2√IoIocosπ4=(2+√2)IoIpointImax=(2+1.414)4=0.853

The path of the difference between two interfering the waves at a point on the screen $\frac{λ}{8}$ . The ratio of intensity at this point and that of at the central fringe will be