question_answer

At the first minimum adjacent to the central maximum of a single slit diffraction pattern, the phase difference between the Huygen’s wavelet from the edge of the slit and the wavelet from the midpoint of the slit is           [NEET (Re) 2015]

A)  \[\frac{\pi }{4}\]radian  

B)  \[\frac{\pi }{2}\]radian

C)  \[\pi \] radian    

D)  \[\frac{\pi }{8}\] radian

Correct Answer: C

Solution :

For first minima at \[P,a\sin \theta =n\lambda \]

where,  \[N=1\Rightarrow a\sin \theta =\lambda ,\]

So, phase difference,

\[\Delta {{\phi }_{1}}=\frac{\Delta {{x}_{1}}}{\lambda }\times 2\pi =\frac{(a/2)\sin \theta }{\lambda }\times 2\pi \]

\[=-\frac{\lambda }{2\lambda }\times 2\pi =\pi \,rad\]