question_answer

In a Young's double slit experiment, the slit separation d is 0.3 mm and the screen distance D is 1 m. A parallel beam of light of wavelength 600 nm is incident on the slits at angle a as shown in figure. On the screen, the point O. is equidistant from the slits and distance PO is 11.0 mm. Which of the following statement(s) is/are correct?

A) Fringe spacing depends on a

B) For \[\alpha =0,\] there will be constructive interference at point P

C) for \[\alpha \,=\,\frac{0.36}{\pi }\]degree, there will be destructive interference at point P.

D) for \[\alpha \,=\,\frac{0.36}{\pi }\] degree, there will be destructive interference at point 0.

Correct Answer: C

Solution :

\[\Delta x=d\,\text{sin}\alpha +d\,\text{sin}\theta \]

\[\theta \alpha :\]small angle

\[\text{sin}\theta =\text{tan}\theta \,=\frac{y}{D}\]

\[\Delta x=d\alpha +\frac{dy}{\text{D}}\]

[a] Fringe width does not depend on a.

[b] \[\Delta x\,=\,0\]

So, constructive interference

[c] \[\Delta x=\,3\text{mn}\times \frac{0.36}{\pi }\times \frac{\pi }{180}+\frac{3\text{mm}\times 11\text{mn}}{1}\,=\,3900\text{nm}\]

\[3900\,\text{nm}\,=\,(2\text{n}-1)\frac{\lambda }{2}=(2\text{n}-1)\times \frac{600\text{nm}}{2}\]

\[n=7\]

Destructive interference happened

[d] \[\Delta x=3\,\text{mm}\times \frac{0.36}{\pi }\times \frac{\pi }{180}+0=600\,\text{nm}\]

\[600\,\text{nm}\,=\,\text{n}\lambda \]

\[n=1\]

Constructive interference.