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In a Young’s double slit experiment, the path difference at a certainpoint on the screen between two interfering waves is 𝟏𝟖th of thewavelength. The ratio of intensity at this point to that at the centreof a bright fringe is close to(i) 0.80(ii) 0.74(iii) 0.94(iv) 0.85

Question

In a Young’s double slit experiment, the path difference at a certainpoint on the screen between two interfering waves is 𝟏𝟖th of thewavelength. The ratio of intensity at this point to that at the centreof a bright fringe is close to(i) 0.80(ii) 0.74(iii) 0.94(iv) 0.85

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Solution

In a Young's double slit experiment, the intensity of light at a point on the screen is given by the formula:

I = I0 [cos^2 (π/2 * δ/λ)]

where I0 is the maximum intensity, δ is the path difference, and λ is the wavelength.

Given that the path difference δ is 1/18th of the wavelength λ, we can substitute δ = λ/18 into the formula:

I = I0 [cos^2 (π/2 * (λ/18) / λ)]

Simplifying, we get:

I = I0 [cos^2 (π/36)]

The cosine of π/36 is approximately 0.9781, so squaring this value gives approximately 0.9566.

Therefore, the ratio of the intensity at this point to the maximum intensity (I/I0) is approximately 0.9566.

So, the closest answer is (iii) 0.94.

This problem has been solved

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