Answer:
The value is [tex]\lambda = 684 \ nm[/tex]
Explanation:
From the question we are told that
The order of the dark fringe is m = 2
The diffraction angle is [tex]\theta = 20^o[/tex]
The diffraction grating is [tex]l = 200\ lines\ per\ mm \ = \ 200000\ lines\ per\ m[/tex]
Generally separation between the slits is mathematically represented as
[tex]d = \frac{1}{ 200000}[/tex]
=> [tex]d = 5 *10^{ -6} \ m[/tex]
Generally the condition for destructive interference is mathematically represented as
[tex]dsin(\theta ) = (m - \frac{1}{2} ) \lambda[/tex]
=> [tex]5 *10^{-6} sin(20) = [2 + \frac{1}{2}] * \lambda[/tex]
=> [tex]\lambda = 684 *10^{-9} \ m[/tex]
=> [tex]\lambda = 684 \ nm[/tex]
