Question

In YDSE experiment screen moves away from slits due to which the point that used to be 2nd maxima is now a point of minima. Here D is initial seperation between slits and screen, then what could be possible displacement of screen?

• A. 2D
• B. 3D
• C. $\frac{D}{3}$
• D. $\frac{D}{8}$

Answer 1

Answer: (B), (C)

The correct options are
B 3D
C $\frac{D}{3}$

Let displacements be $\Delta D$

By $\Delta x=d\tan \theta =d\frac{y}{(D+\Delta D)}$

where $y=\frac{2\lambda D}{d}$
Sicne there is a minima now, $\Delta x=(2n+1)\frac{\lambda }{2}$

$\frac{(2n+1)\lambda }{2}=\frac{d2\lambda D}{d\times (D+\Delta D)}\Rightarrow \Delta D=D(\frac{4}{2n+1}-1)$

$\text{For n = 0,}\Delta D=3D$
$\text{For n = 1,}\Delta D=\frac{D}{3}$
$\text{For n = 2}\text{or greater,}\Delta D<0$