Question

Find the x-coordinates on the x-axis. (excluding $x=0$ and $x=\infty$)

• A. $x=4\lambda$
• B. $x=7\lambda /4$
• C. $x=5\lambda /4$
• D. $x=3\lambda$

Answer 1

Answer: (A), (C)

The correct options are
A $x=4\lambda$
C $x=5\lambda /4$

For bright points, path difference ($S_{2}P-S_{1}P$) must be equal to $n\lambda$.

$\sqrt{9{\lambda }^2+x^2}-x=n\lambda$

$\sqrt{9{\lambda }^2+x^2}=n\lambda +x$

Squaring and solving, $⟹x=\frac{(9-n^2)\lambda }{2n}$

Now for $n=0⟹x=\infty$

For $n=1⟹x=4\lambda$

For $n=2⟹x=\frac{5\lambda }{4}$

For $n=3⟹x=0$