Question

Two coherent sources $S_1$ and $S_2$ are emitting light of wavelength $5000\dot{\text{A}}$ are placed at $0.1\text{mm}$ apart as shown in the figure. A detector is moved along a line perpendicular to $S_1{S}_2$ and passing through $S_1$. The position of the farthest maxima from $S_1$ is approximately at a distance of

• A. $1.2\text{cm}$
• B. $1\text{cm}$
• C. $2\text{cm}$
• D. $1.4\text{cm}$

Answer 1

The correct option is B $1\text{cm}$

At the position of the farthest maxima, the path difference is

$\Delta x=\lambda$

$\Rightarrow S_{2}P-S_{1}P=\lambda$

$\Rightarrow \sqrt{d^2+D^2}-D=\lambda$

$\Rightarrow d^2+D^2=(D+\lambda {)}^2$

$\Rightarrow d^2+D^2=D^2+{\lambda }^2+2\lambda D$

$\Rightarrow 2\lambda D=d^2\left[{\lambda }^2\text{being very small is neglected}\right]$

$\therefore D=\frac{d^2}{2\lambda }=\frac{{10}^{-8}}{2\times 5000\times {10}^{-10}}$

$\Rightarrow D={10}^{-2}\text{m}=1\text{cm}$

Hence, option $\left(\text{B}\right)$ is correct.