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Question

In a double-slit experiment, at a certain point on the screen, the path difference between the two interfering waves is 18 of a wavelength. The ratio of the intensity of light at that point to that at the center of a bright fringe is?


A

0.568

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B

0.853

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C

0.672

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D

0.760

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Solution

The correct option is B

0.853


Step 1:Given data:

In a double-slit experiment, the path difference between the two interfering waves is given as 18 of a wavelength.

Hence, Δx=λ8

Where Δx=Path difference

λ=wavelength of the two interfering waves.

Step 2: Calculating Phase difference :

The phase difference between two waves can be given as:
Phase difference(Δϕ)=2πλ.Δx

Δϕ=2πλ.(λ8)Δϕ=π4

Step 3: Calculating the intensity ratio:

According to the Young's double-slit experiment, we know that at any point, intensity can be given as:

I=Imaxcos2(Δϕ2)

Where, I = Intensity of light at the given point

Imax=The maximum intensity of light at the center of a bright fringe.

Hence, putting all the given values we can calculate the ratio of the intensities of light as:

I=Imaxcos2(π/42)IImax=[cos2(π8)]IImax=(0.9238)2IImax=0.853

Thus, the ratio of the intensity of light at the given point to that at the center of a bright fringe is 0.853. Hence, option B is correct.


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