Q 12-10-079JEE MainJEE Main 2023 (30 Jan, Shift 2)Easy
In a Young's double slit experiment, the intensities at two points, for the path difference $\dfrac\lambda4$ and $\dfrac\lambda3$ ($\lambda$ 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 $\dfrac{I_1+I_2}{I_0}=$ ______.
Numerical value type. Enter your answer.
Answer: 3
$I=4I_0\cos^2\dfrac\phi2$ with $\phi=\dfrac{2\pi}{\lambda}\Delta x$.
$\Delta x=\dfrac\lambda4$: $\phi=\dfrac\pi2$, $I_1=4I_0\cdot\dfrac12=2I_0$.
$\Delta x=\dfrac\lambda3$: $\phi=\dfrac{2\pi}3$, $I_2=4I_0\cdot\dfrac14=I_0$.
$\dfrac{I_1+I_2}{I_0}=3$.
Solution by Sreeraj P, M.Sc Physics