Question

In given YDSE experiment a plane wavefront of $\lambda =600nm$ is incident on slits at angle $\theta ={30}^{\circ }$ as shown in figure. Slit separation is $d=0.5mm$, then

• A. We get maximum intensity at O
• B. Central maxima is $\frac{D}{\sqrt{3}}$ distance above O on screen
• C. Central maxima is $\frac{D}{2}$ distance above O on screen
• D. Intensity at O is not zero

Answer 1

Answer: (B), (D)

The correct options are
B Central maxima is $\frac{D}{\sqrt{3}}$ distance above O on screen
D Intensity at O is not zero


For central maxima

$\Delta x_1=\Delta x_2$

$dsin\theta =dsin\alpha$

$\frac{d}{2}=d\frac{y}{\sqrt{y^2+D^2}}\Rightarrow y^2+D^2=4y^2$

$D^2=3y^2$

$y=\frac{D}{\sqrt{3}}$

Path difference at O is $=\Delta x_1$

$\Delta x_1=dsin\theta =\frac{d}{2}$

If $\Delta x_1=n\lambda$,

$n\times 600nm=\frac{0.5}{2}mm$

On solving, n is not integer i.e. no maxima at O.

Also, $\Delta x_1=(2n-1)\frac{\lambda }{2}$ does not gives n as integer.

So no minima.