Question

A parallel monochromatic beam of light is incident normally on a narrow slit. A diffraction pattern is formed on a screen placed perpendicular to the direction of the incident beam. At the first minimum of the diffraction pattern, the phase difference between the rays coming from the two edges of the slit is

• A. zero
• B. $\pi /2$
• C. $\pi$
• D. $2\pi$

Answer 1

The Correct Option is D

At first minima, b sin $\theta =\lambda$
or $\hspace10mm b \, \theta=\lambda \, or \, \, b \big(\frac{\lambda}{D}\big)=\lambda$
or $\hspace25mm y=\frac{\lambda D}{b}$
or $\hspace25mm \frac{yb}{D}=\lambda \hspace20mm ... (i)$
Now, at P (First minima) path difference between the rays
reaching from two edges (A and B ) will be
$ \, \, \, \, \, \Delta x=\frac{yb}{D} \hspace10mm$(Compare with $\Delta x=\frac{yd}{D}$in YDSE)
or $ \, \, \, \, \Delta x=\lambda \hspace30mm$ [From E (i)]
Corresponding phase difference $(\phi)$ will be
$\hspace15mm \phi=\big(\frac{2 \pi}{\lambda} \big),\Delta x,\phi=\frac{2 \pi}{\lambda}.\lambda=2 \pi$