Explanation:
It is given that,
Wavelength of monochromatic light, [tex]\lambda=600\ nm=6\times 10^{-7}\ m[/tex]
Slits separation, [tex]d=2.2\times 10^{-5}\ m[/tex]
(a) We need to find the angle corresponding to the first bright fringe. For bright fringe the equation is given as :
[tex]d\ sin\theta=n\lambda[/tex], n = 1
[tex]\theta=sin^{-1}(\dfrac{\lambda}{d})[/tex]
[tex]\theta=sin^{-1}(\dfrac{6\times 10^{-7}}{2.2\times 10^{-5}})[/tex]
[tex]\theta=1.56^{\circ}[/tex]
(b) We need to find the angle corresponding to the second dark fringe, n = 1
So, [tex]d\ sin\theta=(n+\dfrac{1}{2})\lambda[/tex]
[tex]sin\theta=\dfrac{3\lambda}{2d}[/tex]
[tex]\theta=sin^{-1}(\dfrac{3\lambda}{2d})[/tex]
[tex]\theta=sin^{-1}(\dfrac{3\times 6\times 10^{-7}}{2\times 2.2\times 10^{-5}})[/tex]
[tex]\theta=2.34^{\circ}[/tex]
Hence, this is the required solution.
