Explanation:
Given that,
Wavelength of the light, [tex]\lambda=691\ nm=691\times 10^{-9}\ m[/tex]
(a) Slit width, [tex]a=3.8\times 10^{-4}\ m[/tex]
The angle that locates the first dark fringe is given by :
[tex]sin\theta=\dfrac{\lambda}{a}[/tex]
[tex]sin\theta=\dfrac{691\times 10^{-9}}{3.8\times 10^{-4}}[/tex]
[tex]\theta=0.104^{\circ}[/tex]
(b) Slit width, [tex]a=3.8\times 10^{-6}\ m[/tex]
The angle that locates the first dark fringe is given by :
[tex]sin\theta=\dfrac{\lambda}{a}[/tex]
[tex]sin\theta=\dfrac{691\times 10^{-9}}{3.8\times 10^{-6}}[/tex]
[tex]\theta=10.47^{\circ}[/tex]
Hence, this is the required solution.
