Optics Question 852
Question: White light used to illuminate the two slits in Young’s double slit experiment. The separation between the slits is d and the distance between the screen and the slit is D(»d). At a point on the screen in front of one of the slits, certain wave- lengths are missing. The missing wavelengths are
Options:
A) $ \lambda =\frac{d^{2}}{(2n+1)D} $
B) $ \lambda =\frac{(2n+1)d^{2}}{D} $
C) $ \lambda =\frac{d^{2}}{(n+1)D} $
D) $ \lambda =\frac{(n+1)D}{d^{2}} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ n^{th} $ minimum has a distance from the centre $ =x=(2n+1)\frac{1}{2}\frac{\lambda D}{d} $ .
For a point on the screen directly in front of one of the slits, $ x=d/2 $
$ \therefore $ for minimum intensity in front of one of the slits $ \frac{d}{2}=(2n+1)\frac{\lambda }{2}\frac{D}{d} $
$ \therefore \lambda =\frac{d^{2}}{(2n+1)D} $
