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                

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