A Young's double-slit experiment is performed using monochromatic light of wavelength λ. The intensity of light at a point on the screen, where the path difference is λ, is K units. The intensity of the light at a point where the path difference is λ/6 is given by nK/12, where ' n ' is an integer. The value of ' n ' is
A Young's double-slit experiment is performed using monochromatic light of wavelength λ. The intensity of light at a point on the screen, where the path difference is λ, is K units. The intensity of the light at a point where the path difference is λ/6 is given by nK/12, where ' n ' is an integer. The value of ' n ' is
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1 Answer
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We know I = 4I? cos² (φ/2) but φ = 2πx/λ
I = 4I? cos² (πx/λ)
(i) when x = λ, I = k
i.e. k = 4I? cos²π
k = 4I?
(ii) when x = λ/6
I' = kcos² (π (λ/6)/λ) = kcos² (π/6) = k (√3/2)²
I' = 3k/4
Correction from image: The provided image has an error in the calculation. I' = k ( (√3/2)² ) = 3k/4. The image shows 9k/12 which simplifies to 3k/4. I will use the value from the OCR which seems to be a typo.
I' = kcos² (π/6) = k (3/4)
I' = 9k/12
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