Question

In the Young's double slit experiment the intestines at two points $P_1$ and $P_2$ on the screen are respectively $I_1$ and $I_2$. If $P_1$ is located at the centre of bright fringe and $P_2$ is located at a distance equal to a quarter of fringe width from $P_1$, then $I_1/I_2$ is

• A. $2$
• B. $1/2$
• C. $4$
• D. $16$

Answer 1

The correct option is A $2$

$\begin{array}{c}{y}_1-y_2=\frac{D\lambda }{4d}\text{, here}\Delta y=\frac{n\Delta \lambda }{d}\\ \text{so}n=\frac{1}{4}\\ \Delta x=\frac{\lambda }{4}\end{array}$

$\begin{array}{c}\varphi =\frac{2\pi }{\lambda }\left(\Delta x\right)=\frac{\pi }{2}\\ I_2=I_1{\cos }^2\frac{\varphi }{2}\\ \Rightarrow \frac{I_1}{I_2}=\frac{1}{{\cos }^2\varphi /2}=2\to \text{Ans}\\ \text{Ans is (A)}\end{array}$