In a Young’s double slit experiment, the intensities at two points, for the path differences λ/4 and λ/3 (λ being the wavelength of light used) are I1 and I2 respectively. If I0 denotes the intensity produced by each one of the individual slits, then I1+I2I0 = ___________.

for I1, ϕ1=2πλ×λ4=π2I1=4I0cos2⁡π4=2I0for I2, ϕ2=2πλ×λ3=2π3I2=4I0cos2⁡π3=I0∴I1+I2I0=3I0I0=3

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In a Young’s double slit experiment, the intensities at two points, for the path differences $λ$ /4 and $λ$ /3 ( $λ$ being the wavelength of light used) are I₁and I₂ respectively. If I₀ denotes the intensity produced by each one of the individual slits, then $\frac{I_{1} + I_{2}}{I_{0}}$ = ___________.

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answer is 3.

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Detailed Solution

for $I_{1}, ϕ_{1} = \frac{2 π}{λ} \times \frac{λ}{4} = \frac{π}{2}$
$I_{1} = 4 I_{0} \cos^{2} \frac{π}{4} = 2 I_{0}$
for $I_{2}, ϕ_{2} = \frac{2 π}{λ} \times \frac{λ}{3} = \frac{2 π}{3} I_{2} = 4 I_{0} \cos^{2} \frac{π}{3} = I_{0}$
$∴ \frac{I_{1} + I_{2}}{I_{0}} = \frac{3 I_{0}}{I_{0}} = 3$