Question

The distance between the two slits in a Young's double slit experiment is $d$ and the distance of the screen from the plane of the slits is $b$,$P$ is a point on the screen directly in front of one of the slits. The path difference between the waves arriving at $P$ from the two slits is

• A. $\frac{d^2}{b}$
• B. $\frac{d^2}{2b}$
• C. $\frac{2d^2}{b}$
• D. $\frac{d^2}{4b}$

Answer 1

The correct option is B $\frac{d^2}{2b}$

Given,

Distance between 2 slit$\left(b\right)$ is $d$

Distance from screen from plane $\left(D\right)$ is $b$

When wave will reach at point P on the screen then path difference is

Path difference$=\frac{yd}{D}$

Here $y$ is slit distance from Centre Therefore $y=d/2$

Substitute all value in above equation

$\frac{\frac{d}{2}\times d}{b}=\frac{d^2}{2b}$

Correct option is B.