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 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
Updated On: Jan 18, 2023
- zero
- $\pi /2$
- $\pi$
- $2\pi$
Show Solution
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The Correct Option is D
Solution and Explanation
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
$\hspace15mm \phi=\big(\frac{2 \pi}{\lambda} \big),\Delta x,\phi=\frac{2 \pi}{\lambda}.\lambda=2 \pi$
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
$\hspace15mm \phi=\big(\frac{2 \pi}{\lambda} \big),\Delta x,\phi=\frac{2 \pi}{\lambda}.\lambda=2 \pi$
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Concepts Used:
Single Slit Diffraction
In the single-slit diffraction experiment, we can examine the bending phenomenon of light or diffraction that causes light from a coherent source to hinder itself and produce an extraordinary pattern on the screen called the diffraction pattern.
Read More: Difference Between Diffraction and Interference
Central Maximum
