In Young’s double-slit experiment using monochromatic light of wavelength λ, the intensity of light at a point on the screen where path difference is λ, is K units. What is the intensity of light at a point where path difference is λ/3?


Given:


Wavelength of monochromatic light = λ


Intensity of light at a point on the screen where path difference is λ = K units.


Intensity of light at any point = I


Intensity of light from slit 1 = I1


Intensity of light from slit 2 = I2


Initially let us consider I1 = I2 = I0


When path difference is λ, the phase difference is 2


Using the formula to find out intensity of resultant wave,


I = I1 + I2 + 2√(I1I2) cos(θ)


k = I0 + I0 + 2 cos π = 4I0 ( Cos(2π) = 1)


k = 4I0


Or, I0 = k/4


When path difference is λ/3, the phase difference is 2/3


I = I1 + I2 + 2√(I1I2) cos(θ)


I = I0 + I0 + 2√(I1I2) cos(2π/3)I0 + I0 + 2I0 × (-1/2) = I0 = k/4


Intensity of light when path difference is λ/3 is k/4.


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