3.In a Young's double slit experiment, the path difference, at a certainpoint on the screen. between two interfering waves is 1/8th ofwavelength. The ratio of the intensity at this point to that at the centreof a bright fringe is close to
Question
3.In a Young's double slit experiment, the path difference, at a certainpoint on the screen. between two interfering waves is 1/8th ofwavelength. The ratio of the intensity at this point to that at the centreof a bright fringe is close to
Solution
In Young's double slit experiment, the intensity of light at a point on the screen is given by the formula:
I = 4I0 cos²(πδ/λ)
where: I0 is the intensity at the center of a bright fringe, δ is the path difference, and λ is the wavelength of light.
Given that the path difference δ is 1/8th of the wavelength (δ = λ/8), we can substitute this into the formula:
I = 4I0 cos²(π(λ/8)/λ) = 4I0 cos²(π/8)
The cosine of π/8 is approximately 0.92388, so squaring this value gives approximately 0.85355.
Therefore, the intensity I at this point is approximately 0.85355 times the intensity I0 at the center of a bright fringe.
So, the ratio of the intensity at this point to that at the center of a bright fringe is close to 0.85355.
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