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
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
Solution
The intensity of light at a point in the interference pattern is given by the formula:
I = I1 + I2 + 2√(I1 * I2) cos φ
where I1 and I2 are the intensities of the two waves, and φ is the phase difference between them.
In a Young's double slit experiment, the path difference δ is related to the phase difference φ by the formula:
φ = 2π * δ / λ
where λ is the wavelength of the light.
Given that the path difference is 1/18 of the wavelength, we can substitute this into the formula to find the phase difference:
φ = 2π * (1/18) = π/9
The intensity at the center of a bright fringe (where the path difference is zero) is given by:
I0 = I1 + I2 + 2√(I1 * I2) = 4I (assuming I1 = I2 = I)
The ratio of the intensity at the point with path difference 1/18 of the wavelength to the intensity at the center of a bright fringe is then:
I/I0 = [I1 + I2 + 2√(I1 * I2) cos(π/9)] / 4I = [2I + 2I cos(π/9)] / 4I = 1/2 + 1/2 cos(π/9)
Using the cosine of π/9 (approximately 0.9848), the ratio is approximately:
1/2 + 1/2 * 0.9848 = 0.7424
So, the ratio of intensity at this point to that at the center of a bright fringe is close to 0.7424.
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