Question

An interference is observed due to two coherent sources 'A' & 'B' separated by a distance of 4$\lambda$ along the y-axis where $\lambda$ is the wavelength of the source. A detector D is moved on the positive x-axis. The number of points on the x-axis excluding the points, x =0 & x =$\infty$ at which maximum will be observed is

• A. three
• B. four
• C. two
• D. infinite

Answer 1

The correct option is A three

From $△ABD$

$(AD{)}^2=(AB{)}^2+(BD{)}^2$

$⟹(AP+PD{)}^2=(AB{)}^2+(BD{)}^2$

Here $AP$ is the path difference.

$\therefore AP=BD=x_n$

$\therefore (n\lambda +x_n{)}^2=(4\lambda {)}^2+(x_n{)}^2$

Or $x_n=\frac{16{\lambda }^2-n^2{\lambda }^2}{2n\lambda }$

$\therefore x_1=\frac{16{\lambda }^2-{\lambda }^2}{2\lambda }=7.5\lambda$

$x_2=\frac{16{\lambda }^2-4{\lambda }^2}{4\lambda }=3\lambda$

$x_3=\frac{16{\lambda }^2-9{\lambda }^2}{6\lambda }=\frac{7}{6}\lambda$

$x_4=0$

No of points where maxima is observed=$3$