Optics Question 163
Question: Two coherent sources S1 and S2 are separated by a distance four times the wavelength l of the source. The sources lie along y axis whereas a detector moves along + x axis. Leaving the origin and far off points the number of points where maxima are observed is
Options:
A) 2
B) 3
C) 4
D) 5
Show Answer
Answer:
Correct Answer: B
Solution:
From $ \Delta S _{1}S _{2}D, $
$ {{(S _{1}D)}^{2}}={{(S _{1}S _{2})}^{2}}+{{(S _{2}D)}^{2}} $
$ {{(S _{1}P+PD)}^{2}}={{(S _{1}S _{2})}^{2}}+{{(S _{2}D)}^{2}} $ .
Here $ S _{1}P $ is the path difference $ =n\lambda $ for maximum intensity.
$ \therefore {{(n\lambda +x _{n})}^{2}}={{(4\lambda )}^{2}}+{{(x _{n})}^{2}} $ or $ x _{n}=\frac{16{{\lambda }^{2}}-n^{2}{{\lambda }^{2}}}{2n\lambda } $ .
Then $ x _{1}=\frac{16{{\lambda }^{2}}-{{\lambda }^{2}}}{2\lambda }=7.5\lambda $
$ x _{2}=\frac{16{{\lambda }^{2}}-4{{\lambda }^{2}}}{4\lambda }=3\lambda $
$ x _{3}=\frac{16{{\lambda }^{2}}-9{{\lambda }^{2}}}{6\lambda }=\frac{7}{6}\lambda $
$ x _{4}=0 $ .
$ \therefore $ Number of points for maxima becomes 3.
