Answer:
[tex]\lambda = 570\ nm[/tex]
Explanation:
Given,
Width of slit, W = 5.7 x 10⁻⁴ m
Distance between central bright fringe, L = 4 m
distance between central bright fringe and first dark fringe, y = 4 mm
Diffraction angle
[tex]tan \theta = \dfrac{y}{L}[/tex]
[tex]tan \theta = \dfrac{4}{4\times 10^3}[/tex]
[tex]\theta = 0.0572[/tex]
Now.
[tex]W sin \theta = m \lambda[/tex]
m = 1
[tex] 5.7 \times 10^{-4} \times sin (0.0572) = 1 \times \lambda[/tex]
[tex]\lambda = 569.99 \times 10^{-9}\ m[/tex]
[tex]\lambda = 570\ nm[/tex]
