Optics Question 871
Question: In YDSE distance between the $ S _{1} $ and $ S _{2} $ is d. $ P _{1} $ and $ P _{2} $ are two points equidistance from O at an angular position $ \beta $ as shown. A parallel beam of monochromatic light is incident at an angle a on the slits. Then the ratio of path difference at $ P _{1} $ and $ P _{2} $ is:
Options:
A) $ \cot \frac{\alpha -\beta }{2}\cot \frac{\alpha +\beta }{2} $
B) $ \tan \frac{\alpha +\beta }{2}\cot \frac{\alpha -\beta }{2} $
C) $ \sin \frac{\alpha +\beta }{2}\cos \frac{\alpha -\beta }{2} $
D) $ \tan \frac{\alpha -\beta }{2}\cot \frac{\alpha +\beta }{2} $
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Answer:
Correct Answer: D
Solution:
[d] $ \frac{\Delta P _{1}}{\Delta P _{2}}=\frac{\sin \alpha -\sin \beta }{\sin \alpha +sin\beta }=\tan \frac{\alpha -\beta }{2}\cot \frac{\alpha +\beta }{2} $
