Q 12-10-123JEE MainJEE Main 2020 (6 Sep, Shift 2)Easy
A Young's double-slit experiment is performed using monochromatic light of wavelength $\lambda$. The intensity of light at a point on the screen, where the path difference is $\lambda$, is $K$ units. The intensity of light at a point where the path difference is $\dfrac\lambda6$ is given by $\dfrac{nK}{12}$, where $n$ is an integer. The value of $n$ is ______.
Numerical value type. Enter your answer.
Answer: 9
$I = I_{\max}\cos^2\dfrac\phi2$. At path difference $\lambda$, $\phi = 2\pi$, so $I_{\max} = K$.
At path difference $\lambda/6$, $\phi = \pi/3$:
$$I = K\cos^2\frac\pi6 = \frac34K = \frac{9K}{12}$$
So $n = 9$.
Solution by Sreeraj P, M.Sc Physics