In a young's double slit experiment, two slits are illuminated by a mixture of two wavelengths 1200nm and 1000nm . At 6.0 mm from the common central bright fringe on a screen 2 m away from the slits, a bright fringe of one interference pattern coincides with the bright fringe of other. Distance between the slits should be
Answer & explanation
Correct answer: option 3
$ x = n\lambda \frac{D}{d} = (n+1)\lambda'\frac{D}{d}$
$1200 n= 1000 (n+1)$
$6n = 5n + 5 \Rightarrow n = 5$
$ x = 5\lambda \frac{D}{d} $
$ d = 5\lambda \frac{D}{x} = 5 \times 1200\times 10^{-9} \frac{2}{6\times 10^{-3}} = 2.0 mm$