In a Young's double slit experiment, the intensities at two points, for the path difference and ( being the wavelength of light used) are and respectively. [2023]

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Solution

Q.
In a Young's double slit experiment, the intensities at two points, for the path difference $\frac{λ}{4}$ and $\frac{λ}{3}$ ( $λ$ being the wavelength of light used) are $I_{1}$ and $I_{2}$ respectively. If $I_{0}$ denotes the intensity produced by each one of the individual slits, then $\frac{I_{1} + I_{2}}{I_{0}} =$ ________ . [2023]

Ans.
(3)

$I = 4 I_{0} \cos^{2} (\frac{Δ ϕ}{2})$

$I_{1} = 4 I_{0} \cos^{2} (\frac{π}{4}) = 2 I_{0}$

$I_{2} = 4 I_{0} \cos^{2} (\frac{2 π}{3}) = I_{0}$

$\Rightarrow \frac{I_{1} + I_{2}}{I_{0}} = 3$

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